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Celebratio Mathematica

Martin Scharlemann

Complete Bibliography

[1] M. G. Schar­le­mann and L. C. Sieben­mann: “The Hauptver­mu­tung for \( C^{\infty} \) homeo­morph­isms, II: A proof val­id for open 4-man­i­folds,” Com­posi­tio Math. 29 : 3 (1974), pp. 253–​264. MR 375338 Zbl 0315.​57010 article

[2] M. G. Schar­le­mann: A fake ho­mo­topy struc­ture on \( S^3\times S^1\mathbin{\#} S^1\times S^2 \) and a struc­ture the­or­em for five-man­i­folds. Ph.D. thesis, Uni­versity of Cali­for­nia, Berke­ley, 1974. Ad­vised by R. Kirby. MR 2940416 phdthesis

[3]R. C. Kirby and M. G. Schar­le­mann: “A curi­ous cat­egory which equals TOP,” pp. 93–​97 in Man­i­folds—Tokyo 1973. Edi­ted by A. Hat­tori. Univ. Tokyo Press (Tokyo), 1975. MR 0372868 Zbl 0315.​57003

[4] M. G. Schar­le­mann and L. C. Sieben­mann: “The Hauptver­mu­tung for smooth sin­gu­lar homeo­morph­isms,” pp. 85–​91 in Man­i­folds — Tokyo 1973 (Tokyo, 10–17 April 1973). Edi­ted by A. Hat­tori. Uni­versity of Tokyo Press, 1975. A part II (with some­what dif­fer­ent title) was pub­lished in Com­posi­tio Math. 29:3 (1974). MR 372871 Zbl 0315.​57009 incollection

[5] M. Schar­le­mann: “Equi­val­ence of 5-di­men­sion­al \( s \)-cobor­d­isms,” Proc. Amer. Math. Soc. 53 : 2 (December 1975), pp. 508–​510. MR 380838 Zbl 0285.​57020 article

[6] M. Schar­le­mann: “Con­struct­ing strange man­i­folds with the do­deca­hed­ral space,” Duke Math. J. 43 : 1 (March 1976), pp. 33–​40. MR 402760 Zbl 0331.​57007 article

[7] M. G. Schar­le­mann: “Trans­vers­al­ity the­or­ies at di­men­sion four,” In­vent. Math. 33 : 1 (February 1976), pp. 1–​14. MR 410756 Zbl 0318.​57007 article

[8] M. Schar­le­mann: “Sim­pli­cial tri­an­gu­la­tion of non­com­bin­at­or­i­al man­i­folds of di­men­sion less than 9,” Trans. Amer. Math. Soc. 219 (May 1976), pp. 269–​287. MR 415629 Zbl 0333.​57009 article

[9] M. Schar­le­mann: “The fun­da­ment­al group of fibered knot cobor­d­isms,” Math. Ann. 225 : 3 (October 1977), pp. 243–​251. MR 428338 Zbl 0325.​55001 article

[10] M. Schar­le­mann: “Thor­oughly knot­ted ho­mo­logy spheres,” Hou­s­ton J. Math. 3 : 2 (1977), pp. 271–​283. MR 442947 Zbl 0355.​57011 article

[11] M. Schar­le­mann: “Iso­topy and cobor­d­ism of ho­mo­logy spheres in spheres,” J. Lon­don Math. Soc. (2) 16 : 3 (December 1977), pp. 559–​567. MR 464246 Zbl 0375.​57003 article

[12] M. Schar­le­mann: “Non-PL im­bed­dings of 3-man­i­folds,” Amer. J. Math. 100 : 3 (June 1978), pp. 539–​545. MR 515651 Zbl 0386.​57009 article

[13] M. Schar­le­mann: “Smooth CE maps and smooth homeo­morph­isms,” pp. 234–​240 in Al­geb­ra­ic and geo­met­ric to­po­logy: Pro­ceed­ings of a sym­posi­um held at Santa Bar­bara in hon­or of Ray­mond L. Wilder (Santa Bar­bara, CA, 25–29 Ju­ly 1977). Edi­ted by K. C. Mil­lett. Lec­ture Notes in Math­em­at­ics 664. Spring­er (Ber­lin), 1978. MR 518417 Zbl 0392.​57002 incollection

[14]R. C. Kirby and M. G. Schar­le­mann: “Eight faces of the Poin­caré ho­mo­logy 3-sphere,” pp. 113–​146 in Geo­met­ric to­po­logy (Athens, GA, 1977). Edi­ted by J. C. Cantrell. Aca­dem­ic Press (New York), 1979. MR 537730 Zbl 0469.​57006

[15] M. Schar­le­mann: “Trans­verse White­head tri­an­gu­la­tions,” Pac. J. Math. 80 : 1 (September 1979), pp. 245–​251. MR 534713 Zbl 0419.​57003 article

[16] M. Schar­le­mann: “Ap­prox­im­at­ing \( \mathit{CAT} \) CE maps by \( \mathit{CAT} \) homeo­morph­isms,” pp. 475–​501 in Geo­met­ric to­po­logy (Athens, GA, 1–12 Au­gust 1977). Edi­ted by J. C. Cantrell. Aca­dem­ic Press (New York and Lon­don), 1979. MR 537746 Zbl 0474.​57010 incollection

[17] M. Schar­le­mann: “Sub­groups of \( \mathrm{SL}(2,\mathbf{R}) \) freely gen­er­ated by three para­bol­ic ele­ments,” Lin­ear and Mul­ti­lin­ear Al­gebra 7 : 3 (1979), pp. 177–​191. MR 540952 Zbl 0412.​20033 article

[18] M. Schar­le­mann: “The sub­group of \( \Delta_{2} \) gen­er­ated by auto­morph­isms of tori,” Math. Ann. 251 : 3 (1980), pp. 263–​268. MR 589255 article

[19]R. C. Kirby and M. G. Schar­le­mann: “Eight faces of the Poin­caré ho­mo­logy 3-sphere,” Us­pekhi Mat. Nauk 37 : 5(227) (1982), pp. 139–​159. MR 676615 Zbl 0511.​57008

[20] M. Schar­le­mann: “The com­plex of curves on nonori­ent­able sur­faces,” J. Lon­don Math. Soc. (2) 25 : 1 (February 1982), pp. 171–​184. MR 645874 Zbl 0479.​57005 article

[21] M. Schar­le­mann: “Es­sen­tial tori in 4-man­i­fold bound­ar­ies,” Pac. J. Math. 105 : 2 (October 1983), pp. 439–​447. MR 691614 Zbl 0516.​57007 article

[22] M. Schar­le­mann and C. Squier: “Auto­morph­isms of the free group of rank two without fi­nite or­bits,” pp. 341–​346 in Low-di­men­sion­al to­po­logy (San Fran­cisco, CA, 7–11 Janu­ary 1981). Edi­ted by S. J. Lomonaco. Con­tem­por­ary Math­em­at­ics 20. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1983. MR 718151 Zbl 0523.​57002 incollection

[23] M. Schar­le­mann: “The four-di­men­sion­al Schoen­flies con­jec­ture is true for genus two im­bed­dings,” To­po­logy 23 : 2 (1984), pp. 211–​217. MR 744851 Zbl 0543.​57011 article

[24] M. Schar­le­mann: “Tun­nel num­ber one knots sat­is­fy the Poen­aru con­jec­ture,” To­po­logy Ap­pl. 18 : 2–​3 (December 1984), pp. 235–​258. MR 769294 Zbl 0592.​57004 article

[25] M. Schar­le­mann: “Smooth spheres in \( \mathbf{R}^4 \) with four crit­ic­al points are stand­ard,” In­vent. Math. 79 : 1 (February 1985), pp. 125–​141. MR 774532 Zbl 0559.​57019 article

[26] M. G. Schar­le­mann: “Un­knot­ting num­ber one knots are prime,” In­vent. Math. 82 : 1 (February 1985), pp. 37–​55. MR 808108 Zbl 0576.​57004 article

[27] M. Schar­le­mann: “Out­er­most forks and a the­or­em of Jaco,” pp. 189–​193 in Com­bin­at­or­i­al meth­ods in to­po­logy and al­geb­ra­ic geo­metry (Rochester, NY, 29 June–2 Ju­ly 1982). Edi­ted by J. R. Harp­er and R. Man­del­baum. Con­tem­por­ary Math­em­at­ics 44. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1985. Con­fer­ence in hon­or of Ar­thur M. Stone. MR 813113 Zbl 0589.​57011 incollection

[28] M. Schar­le­mann: “3-man­i­folds with \( H_2(A,\partial A)=0 \) and a con­jec­ture of Stallings,” pp. 138–​145 in Knot the­ory and man­i­folds (Van­couver, BC, 2–4 June 1983). Edi­ted by D. Rolf­sen. Lec­ture Notes in Math­em­at­ics 1144. Spring­er (Ber­lin), 1985. MR 823287 Zbl 0585.​57011 incollection

[29] S. Bleiler and M. Schar­le­mann: “Tangles, prop­erty \( P \), and a prob­lem of J. Mar­tin,” Math. Ann. 273 : 2 (June 1986), pp. 215–​225. MR 817877 Zbl 0563.​57002 article

[30] M. Schar­le­mann: “A re­mark on com­pan­ion­ship and prop­erty P,” Proc. Amer. Math. Soc. 98 : 1 (1986), pp. 169–​170. MR 848897 Zbl 0602.​57006 article

[31] M. Schar­le­mann: “The Thur­ston norm and 2-handle ad­di­tion,” Proc. Amer. Math. Soc. 100 : 2 (June 1987), pp. 362–​366. MR 884480 Zbl 0627.​57010 article

[32] M. Schar­le­mann and A. Thompson: “Find­ing dis­joint Seifert sur­faces,” Bull. Lon­don Math. Soc. 20 : 1 (January 1988), pp. 61–​64. MR 916076 Zbl 0654.​57005 article

[33] M. Schar­le­mann and A. Thompson: “Un­knot­ting num­ber, genus, and com­pan­ion tori,” Math. Ann. 280 : 2 (1988), pp. 191–​205. MR 929535 Zbl 0616.​57003 article

[34] S. Bleiler and M. Schar­le­mann: “A pro­ject­ive plane in \( \mathbb{R}^4 \) with three crit­ic­al points is stand­ard. Strongly in­vert­ible knots have prop­erty \( P \),” To­po­logy 27 : 4 (1988), pp. 519–​540. MR 976593 Zbl 0678.​57003 article

[35] M. Schar­le­mann and A. Thompson: “Link genus and the Con­way moves,” Com­ment. Math. Helv. 64 : 4 (December 1989), pp. 527–​535. MR 1022995 Zbl 0693.​57004 article

[36] M. Schar­le­mann: “Su­tured man­i­folds and gen­er­al­ized Thur­ston norms,” J. Diff. Geom. 29 : 3 (1989), pp. 557–​614. MR 992331 Zbl 0673.​57015 article

[37] M. Schar­le­mann: “Pro­du­cing re­du­cible 3-man­i­folds by sur­gery on a knot,” To­po­logy 29 : 4 (1990), pp. 481–​500. MR 1071370 Zbl 0727.​57015 article

[38] M. G. Schar­le­mann: “Lec­tures on the the­ory of su­tured 3-man­i­folds,” pp. 25–​45 in Al­gebra and to­po­logy 1990 (Tae­jon, S. Korea, 8–11 Au­gust 1990). Edi­ted by S. H. Bae and G. T. Jin. Korea Ad­vanced In­sti­tute of Sci­ence and Tech­no­logy (Tae­jon), 1990. MR 1098719 Zbl 0756.​57007 incollection

[39] M. Schar­le­mann and A. Thompson: “De­tect­ing un­knot­ted graphs in 3-space,” J. Diff. Geom. 34 : 2 (1991), pp. 539–​560. MR 1131443 Zbl 0751.​05033 article

[40] M. Schar­le­mann: “Handle­body com­ple­ments in the 3-sphere: A re­mark on a the­or­em of Fox,” Proc. Amer. Math. Soc. 115 : 4 (August 1992), pp. 1115–​1117. MR 1116272 Zbl 0759.​57012 article

[41] M. Schar­le­mann: “Some pictori­al re­marks on Su­zuki’s Brun­ni­an graph,” pp. 351–​354 in To­po­logy ’90 (Colum­bus, OH, Feb­ru­ary–June 1990). Edi­ted by B. Apanasov, W. D. Neu­mann, A. W. Re­id, and L. Sieben­mann. Ohio State Uni­versity Math­em­at­ics Re­search In­sti­tute Pub­lic­a­tions 1. de Gruyter (Ber­lin), 1992. MR 1184420 Zbl 0772.​57005 incollection

[42] M. Schar­le­mann: “To­po­logy of knots,” pp. 65–​82 in To­po­lo­gic­al as­pects of the dy­nam­ics of flu­ids and plas­mas (Santa Bar­bara, CA, Au­gust–Decem­ber 1991). Edi­ted by H. K. Mof­fatt, G. M. Zaslavsky, P. Comte, and M. Tabor. NATO ASI Series. Series E. Ap­plied Sci­ence 218. Kluwer Aca­dem­ic (Dordrecht), 1992. MR 1232225 Zbl 0799.​57003 incollection

[43] M. Schar­le­mann: “Un­link­ing via sim­ul­tan­eous cross­ing changes,” Trans. Amer. Math. Soc. 336 : 2 (1993), pp. 855–​868. MR 1200011 Zbl 0785.​57003 article

[44] M. Schar­le­mann and A. Thompson: “Hee­gaard split­tings of \( (\mathrm{surface})\times I \) are stand­ard,” Math. Ann. 295 : 3 (January 1993), pp. 549–​564. MR 1204837 Zbl 0814.​57010 article

[45] M. Schar­le­mann and Y. Q. Wu: “Hy­per­bol­ic man­i­folds and de­gen­er­at­ing handle ad­di­tions,” J. Aus­tral. Math. Soc. Ser. A 55 : 1 (August 1993), pp. 72–​89. MR 1231695 Zbl 0802.​57005 article

[46] M. Schar­le­mann and A. Thompson: “Thin po­s­i­tion and Hee­gaard split­tings of the 3-sphere,” J. Diff. Geom. 39 : 2 (1994), pp. 343–​357. MR 1267894 Zbl 0820.​57005 article

[47] M. Schar­le­mann and A. Thompson: “Thin po­s­i­tion for 3-man­i­folds,” pp. 231–​238 in Geo­met­ric to­po­logy (Haifa, Is­rael, 10–16 June 1992). Edi­ted by C. Gor­don, Y. Mori­ah, and B. Wa­jnryb. Con­tem­por­ary Math­em­at­ics 164. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1994. MR 1282766 Zbl 0818.​57013 incollection

[48] M. Schar­le­mann and A. Thompson: “Push­ing arcs and graphs around in handle­bod­ies,” pp. 163–​171 in Low-di­men­sion­al to­po­logy (Knoxville, TN, 18–25 May 1992). Edi­ted by K. Jo­hann­son. Con­fer­ence Pro­ceed­ings and Lec­ture Notes in Geo­metry and To­po­logy 3. In­ter­na­tion­al Press (Cam­bridge, MA), 1994. MR 1316180 Zbl 0868.​57024 incollection

[49]H. Ru­bin­stein and M. Schar­le­mann: “Com­par­ing Hee­gaard split­tings of non-Haken 3-man­i­folds,” To­po­logy 35 : 4 (October 1996), pp. 1005–​1026. MR 1404921 Zbl 0858.​57020 article

[50] A. Bart and M. Schar­le­mann: “Least weight in­ject­ive sur­faces are fun­da­ment­al,” To­po­logy Ap­pl. 69 : 3 (April 1996), pp. 251–​264. MR 1382295 Zbl 0858.​57016 article

[51]H. Ru­bin­stein and M. Schar­le­mann: “Trans­verse Hee­gaard split­tings,” Mich. Math. J. 44 : 1 (1997), pp. 69–​83. MR 1439669 Zbl 0907.​57013 article

[52] M. Schar­le­mann: “Planar graphs, fam­ily trees and braids,” pp. 29–​47 in Pro­gress in knot the­ory and re­lated top­ics (Mar­seilles). Edi­ted by M. Boileau, M. Domergue, Y. Math­ieu, and K. Mil­lett. Travaux en Cours 56. Her­mann (Par­is), 1997. MR 1603122 Zbl 0924.​57002 incollection

[53]H. Ru­bin­stein and M. Schar­le­mann: “Com­par­ing Hee­gaard split­tings: The bounded case,” Trans. Am. Math. Soc. 350 : 2 (1998), pp. 689–​715. MR 1401528 Zbl 0892.​57009 article

[54] M. Schar­le­mann: “Cross­ing changes,” Chaos Solitons Fractals 9 : 4–​5 (April–May 1998), pp. 693–​704. Knot the­ory and its ap­plic­a­tions. MR 1628751 Zbl 0937.​57004 article

[55] M. Schar­le­mann: “Loc­al de­tec­tion of strongly ir­re­du­cible Hee­gaard split­tings,” To­po­logy Ap­pl. 90 : 1–​3 (December 1998), pp. 135–​147. MR 1648310 Zbl 0926.​57018 article

[56]Pro­ceed­ings of the Kirby­fest (Berke­ley, CA, June 22–26, 1998). Edi­ted by J. Hass and M. Schar­le­mann. Geo­metry & To­po­logy Mono­graphs 2. Geo­metry & To­po­logy Pub­lic­a­tions (Cov­entry), 1999. MR 1734398

[57]H. Ru­bin­stein and M. Schar­le­mann: “Genus two Hee­gaard split­tings of ori­ent­able three-man­i­folds,” pp. 489–​553 in Pro­ceed­ings of the Kirby­Fest (Berke­ley, CA, 22–26 June 1998). Edi­ted by J. Hass and M. Schar­le­mann. Geo­metry & To­po­logy Mono­graphs 2. In­ter­na­tion­al Press (Cam­bridge, MA), 1999. Pa­pers ded­ic­ated to Rob Kirby on the oc­ca­sion of his 60th birth­day. MR 1734422 Zbl 0962.​57013 ArXiv 9712262 incollection

[58] M. Schar­le­mann and J. Schul­tens: “The tun­nel num­ber of the sum of \( n \) knots is at least \( n \),” To­po­logy 38 : 2 (March 1999), pp. 265–​270. MR 1660345 Zbl 0929.​57003 article

[59] D. Cooper and M. Schar­le­mann: “The struc­ture of a solv­man­i­fold’s Hee­gaard split­tings,” pp. 1–​18 in Pro­ceed­ings of 6th Gökova geo­metry-to­po­logy con­fer­ence (Gökova, Tur­key, 25–29 May 1998), published as Turk­ish J. Math. 23 : 1. Issue edi­ted by S. Ak­bu­lut, T. Önder, and R. J. Stern. Sci­entif­ic and Tech­nic­al Re­search Coun­cil of Tur­key (Ank­ara), 1999. Ded­ic­ated to Rob Kirby on the oc­ca­sion of his 60th birth­day. MR 1701636 Zbl 0948.​57015 incollection

[60] M. Schar­le­mann and J. Schul­tens: “An­nuli in gen­er­al­ized Hee­gaard split­tings and de­gen­er­a­tion of tun­nel num­ber,” Math. Ann. 317 : 4 (2000), pp. 783–​820. MR 1777119 Zbl 0953.​57002 article

[61] H. Goda, M. Schar­le­mann, and A. Thompson: “Lev­el­ling an un­knot­ting tun­nel,” Geom. To­pol. 4 (2000), pp. 243–​275. MR 1778174 Zbl 0958.​57007 ArXiv math.​GT/​9910099 article

[62] M. Schar­le­mann and J. Schul­tens: “Com­par­ing Hee­gaard and JSJ struc­tures of ori­ent­able 3-man­i­folds,” Trans. Amer. Math. Soc. 353 : 2 (2001), pp. 557–​584. MR 1804508 Zbl 0959.​57010 article

[63] M. Jones and M. Schar­le­mann: “How a strongly ir­re­du­cible Hee­gaard split­ting in­ter­sects a handle­body,” To­po­logy Ap­pl. 110 : 3 (March 2001), pp. 289–​301. MR 1807469 Zbl 0974.​57011 article

[64] M. Schar­le­mann: “Hee­gaard re­du­cing spheres for the 3-sphere,” Rend. Istit. Mat. Univ. Trieste 32 : supplement 1 (2001), pp. 397–​410. Ded­ic­ated to the memory of Marco Reni. MR 1893407 Zbl 1030.​57031 article

[65] M. Schar­le­mann: “The Goda–Ter­agaito con­jec­ture: An over­view,” pp. 87–​102 in On Hee­gaard split­tings and Dehn sur­ger­ies of 3-man­i­folds, and top­ics re­lated to them (Kyoto, 11–15 June 2001), published as RIMS Kōkyūroku 1229. Issue edi­ted by T. Kobay­ashi. 2001. MR 1905564 incollection

[66] M. Schar­le­mann: “Hee­gaard split­tings of com­pact 3-man­i­folds,” pp. 921–​953 in Hand­book of geo­met­ric to­po­logy. Edi­ted by R. J. Dav­er­man and R. B. Sher. North-Hol­land (Am­s­ter­dam), 2002. MR 1886684 Zbl 0985.​57005 ArXiv math/​0007144 incollection

[67] M. Schar­le­mann and A. Thompson: “Un­knot­ting tun­nels and Seifert sur­faces,” Proc. Lon­don Math. Soc. (3) 87 : 2 (September 2003), pp. 523–​544. MR 1990938 Zbl 1047.​57008 article

[68] M. Schar­le­mann and A. Thompson: “Thin­ning genus two Hee­gaard spines in \( S^3 \),” J. Knot The­or. Ramif. 12 : 5 (August 2003), pp. 683–​708. MR 1999638 Zbl 1048.​57002 article

[69] M. Schar­le­mann: “Hee­gaard split­tings of 3-man­i­folds,” pp. 25–​39 in Low di­men­sion­al to­po­logy: Lec­tures at the Morn­ing­side Cen­ter of Math­em­at­ics (Beijing, 1998–1999). Edi­ted by B. Li, S. Wang, and X. Zhao. New Stud­ies in Ad­vanced Math­em­at­ics 3. In­ter­na­tion­al Press (Somerville, MA), 2003. MR 2052244 Zbl 1044.​57006 incollection

[70] M. Schar­le­mann: “There are no un­ex­pec­ted tun­nel num­ber one knots of genus one,” Trans. Amer. Math. Soc. 356 : 4 (2004), pp. 1385–​1442. MR 2034312 Zbl 1042.​57003 article

[71] M. Schar­le­mann and A. Thompson: “On the ad­dit­iv­ity of knot width,” pp. 135–​144 in Pro­ceed­ings of the Cas­son Fest (Fay­etteville, AR, 10–12 April 2003 and Aus­tin, TX, 19–21 May 2003). Edi­ted by C. Gor­don and Y. Rieck. Geo­metry and To­po­logy Mono­graphs 7. Geo­metry & To­po­logy Pub­lic­a­tions (Cov­entry, UK), 2004. MR 2172481 Zbl 1207.​57016 incollection

[72] M. Schar­le­mann: “Auto­morph­isms of the 3-sphere that pre­serve a genus two Hee­gaard split­ting,” Bol. Soc. Mat. Mex­ic­ana (3) 10 : special issue (2004), pp. 503–​514. MR 2199366 Zbl 1095.​57017 ArXiv math/​0307231 article

[73] M. Schar­le­mann and A. Thompson: “Sur­faces, sub­man­i­folds, and aligned Fox re­imbed­ding in non-Haken 3-man­i­folds,” Proc. Amer. Math. Soc. 133 : 6 (2005), pp. 1573–​1580. MR 2120271 Zbl 1071.​57015 article

[74] M. Schar­le­mann: “Thin po­s­i­tion in the the­ory of clas­sic­al knots,” Chapter 9, pp. 429–​459 in Hand­book of knot the­ory. Edi­ted by W. Menasco and M. Thistleth­waite. El­sevi­er (Am­s­ter­dam), 2005. MR 2179267 Zbl 1097.​57013 incollection

[75] M. Schar­le­mann and J. Schul­tens: “3-man­i­folds with planar present­a­tions and the width of satel­lite knots,” Trans. Amer. Math. Soc. 358 : 9 (2006), pp. 3781–​3805. MR 2218999 Zbl 1102.​57004 article

[76] M. Schar­le­mann and M. To­mova: “Al­tern­ate Hee­gaard genus bounds dis­tance,” Geom. To­pol. 10 (2006), pp. 593–​617. MR 2224466 Zbl 1128.​57022 article

[77] M. Schar­le­mann: “Prox­im­ity in the curve com­plex: Bound­ary re­duc­tion and bicom­press­ible sur­faces,” Pac. J. Math. 228 : 2 (December 2006), pp. 325–​348. MR 2274524 Zbl 1127.​57010 article

[78] M. Schar­le­mann: “Gen­er­al­ized prop­erty \( R \) and the Schoen­flies con­jec­ture,” Com­ment. Math. Helv. 83 : 2 (2008), pp. 421–​449. MR 2390052 Zbl 1148.​57032 article

[79] M. Schar­le­mann and M. To­mova: “Unique­ness of bridge sur­faces for 2-bridge knots,” Math. Proc. Cam­bridge Philos. Soc. 144 : 3 (May 2008), pp. 639–​650. MR 2418708 Zbl 1152.​57006 article

[80] M. Schar­le­mann and M. To­mova: “Con­way products and links with mul­tiple bridge sur­faces,” Mich. Math. J. 56 : 1 (2008), pp. 113–​144. MR 2433660 Zbl 1158.​57011 article

[81] The Zi­eschang Gedenk­s­chrift: A me­mori­al volume for Hein­er Zi­eschang (1936–2004). Edi­ted by M. Boileau, M. Schar­le­mann, and R. Weidmann. Geo­metry and To­po­logy Mono­graphs 14. Geo­metry & To­po­logy Pub­lic­a­tions (Cov­entry, UK), 2008. MR 2484694 Zbl 1135.​00012 book

[82] M. Schar­le­mann: “Re­filling me­ridi­ans in a genus 2 handle­body com­ple­ment,” pp. 451–​475 in The Zi­eschang Gedenk­s­chrift: A me­mori­al volume for Hein­er Zi­eschang (1936–2004). Edi­ted by M. Boileau, M. Schar­le­mann, and R. Weidmann. Geo­metry and To­po­logy Mono­graphs 14. Geo­metry & To­po­logy Pub­lic­a­tions (Cov­entry, UK), 2008. Ded­ic­ated to the memory of Hein­er Zi­eschang, first to no­tice that genus two handle­bod­ies could be in­ter­est­ing. MR 2484713 Zbl 1177.​57019 incollection

[83] M. Schar­le­mann and A. A. Thompson: “Sur­gery on a knot in (sur­face \( \times I \)),” Al­gebr. Geom. To­pol. 9 : 3 (2009), pp. 1825–​1835. MR 2550096 Zbl 1197.​57011 article

[84] R. Qiu and M. Schar­le­mann: “A proof of the Gor­don con­jec­ture,” Adv. Math. 222 : 6 (December 2009), pp. 2085–​2106. MR 2562775 Zbl 1180.​57025 article

[85] R. E. Gom­pf, M. Schar­le­mann, and A. Thompson: “Fibered knots and po­ten­tial counter­examples to the prop­erty 2R and slice-rib­bon con­jec­tures,” Geom. To­pol. 14 : 4 (2010), pp. 2305–​2347. MR 2740649 Zbl 1214.​57008 article

[86] M. Schar­le­mann: “An over­view of Prop­erty 2R,” pp. 317–​325 in The math­em­at­ics of knots. Edi­ted by M. Banagl and D. Vo­gel. Con­tri­bu­tions in Math­em­at­ic­al and Com­pu­ta­tion­al Sci­ences 1. Spring­er (Ber­lin), 2011. MR 2777854 Zbl 1221.​57012 incollection

[87] J. Berge and M. Schar­le­mann: “Mul­tiple genus 2 Hee­gaard split­tings: A missed case,” Al­gebr. Geom. To­pol. 11 : 3 (2011), pp. 1781–​1792. MR 2821441 Zbl 1232.​57020 article

[88] M. Schar­le­mann: “Berge’s dis­tance 3 pairs of genus 2 Hee­gaard split­tings,” Math. Proc. Cam­bridge Philos. Soc. 151 : 2 (September 2011), pp. 293–​306. MR 2823137 Zbl 1226.​57033 article

[89] M. Schar­le­mann: “Gen­er­at­ing the genus \( g+1 \) Goer­itz group of a genus \( g \) handle­body,” pp. 347–​369 in Geo­metry and to­po­logy down un­der (Mel­bourne, 11–22 Ju­ly 2011). Edi­ted by C. D. Hodg­son, W. H. Jaco, M. G. Schar­le­mann, and S. Till­mann. Con­tem­por­ary Math­em­at­ics 597. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2013. MR 3186683 Zbl 1288.​57014 incollection

[90] Geo­metry and to­po­logy down un­der: A con­fer­ence in hon­our of Hyam Ru­bin­stein (Mel­bourne, Aus­tralia, 11–22 Ju­ly 2011). Edi­ted by C. D. Hodg­son, W. H. Jaco, M. G. Schar­le­mann, and S. Till­mann. Con­tem­por­ary Math­em­at­ics 597. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2013. MR 3202515 Zbl 1272.​57002 book

[91] M. Schar­le­mann, J. Schul­tens, and T. Saito: Lec­ture notes on gen­er­al­ized Hee­gaard split­tings (Kyoto, 11–15 June 2001). World Sci­entif­ic (Hack­en­sack, NJ), 2016. Three lec­tures on low-di­men­sion­al to­po­logy in Kyoto. MR 3585907 Zbl 1356.​57004 book

[92] M. Schar­le­mann: “Pro­posed Prop­erty 2R counter­examples ex­amined,” Ill. J. Math. 60 : 1 (2016), pp. 207–​250. To Wolfgang Haken, who, forty years ago, found that Four Col­ors Suf­fice. MR 3665179 Zbl 1376.​57012 article

[93] M. Freed­man and M. Schar­le­mann: Pow­ell moves and the Goer­itz group. Pre­print, 2018. ArXiv 1804.​05909 techreport

[94] M. Freed­man and M. Schar­le­mann: “Dehn’s lemma for im­mersed loops,” Math. Res. Lett. 25 : 6 (2018), pp. 1827–​1836. MR 3934846 article

[95] M. Schar­le­mann: A strong Haken’s The­or­em. Pre­print, 2020. ArXiv 2003.​08523 techreport

[96] M. Freed­man and M. Schar­le­mann: Unique­ness in Haken’s The­or­em. Pre­print, 2020. ArXiv 2004.​07385 techreport