### Complete Bibliography

[1]
:
“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]
:
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] : “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]
:
“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]
:
“Equivalence of 5-dimensional __\( s \)__-cobordisms,”
Proc. Amer. Math. Soc.
53 : 2
(December 1975),
pp. 508–510.
MR
380838
Zbl
0285.57020
article

[6] : “Constructing strange manifolds with the dodecahedral space,” Duke Math. J. 43 : 1 (March 1976), pp. 33–40. MR 402760 Zbl 0331.57007 article

[7] : “Transversality theories at dimension four,” Invent. Math. 33 : 1 (February 1976), pp. 1–14. MR 410756 Zbl 0318.57007 article

[8] : “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] : “The fundamental group of fibered knot cobordisms,” Math. Ann. 225 : 3 (October 1977), pp. 243–251. MR 428338 Zbl 0325.55001 article

[10] : “Thoroughly knotted homology spheres,” Houston J. Math. 3 : 2 (1977), pp. 271–283. MR 442947 Zbl 0355.57011 article

[11] : “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] : “Non-PL imbeddings of 3-manifolds,” Amer. J. Math. 100 : 3 (June 1978), pp. 539–545. MR 515651 Zbl 0386.57009 article

[13] : “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] : “Transverse Whitehead triangulations,” Pac. J. Math. 80 : 1 (September 1979), pp. 245–251. MR 534713 Zbl 0419.57003 article

[15] : “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

[16]
:
“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]
:
“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]
:
“The subgroup of __\( \Delta_{2} \)__ generated by automorphisms
of tori,”
Math. Ann.
251 : 3
(1980),
pp. 263–268.
MR
589255
article

[19] : “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

[20] : “Eight faces of the Poincaré homology 3-sphere,” Uspekhi Mat. Nauk 37 : 5(227) (1982), pp. 139–159. MR 676615 Zbl 0511.57008

[21] : “Essential tori in 4-manifold boundaries,” Pac. J. Math. 105 : 2 (October 1983), pp. 439–447. MR 691614 Zbl 0516.57007 article

[22] : “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] : “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] : “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]
:
“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] : “Unknotting number one knots are prime,” Invent. Math. 82 : 1 (February 1985), pp. 37–55. MR 808108 Zbl 0576.57004 article

[27] : “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]
:
“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]
:
“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] : “A remark on companionship and property P,” Proc. Amer. Math. Soc. 98 : 1 (1986), pp. 169–170. MR 848897 Zbl 0602.57006 article

[31] : “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] : “Finding disjoint Seifert surfaces,” Bull. London Math. Soc. 20 : 1 (January 1988), pp. 61–64. MR 916076 Zbl 0654.57005 article

[33] : “Unknotting number, genus, and companion tori,” Math. Ann. 280 : 2 (March 1988), pp. 191–205. MR 929535 Zbl 0616.57003 article

[34]
:
“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] : “Link genus and the Conway moves,” Comment. Math. Helv. 64 : 4 (1989), pp. 527–535. MR 1022995 Zbl 0693.57004 article

[36] : “Sutured manifolds and generalized Thurston norms,” J. Diff. Geom. 29 : 3 (1989), pp. 557–614. MR 992331 Zbl 0673.57015 article

[37] : “Producing reducible 3-manifolds by surgery on a knot,” Topology 29 : 4 (1990), pp. 481–500. MR 1071370 Zbl 0727.57015 article

[38] : “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] : “Detecting unknotted graphs in 3-space,” J. Diff. Geom. 34 : 2 (1991), pp. 539–560. MR 1131443 Zbl 0751.05033 article

[40] : “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] : “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] : “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] : “Unlinking via simultaneous crossing changes,” Trans. Amer. Math. Soc. 336 : 2 (1993), pp. 855–868. MR 1200011 Zbl 0785.57003 article

[44]
:
“Heegaard splittings of __\( (\textrm{surface})\times I \)__ are standard,”
Math. Ann.
295 : 3
(1993),
pp. 549–564.
MR
1204837
Zbl
0814.57010
article

[45] : “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] : “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] : “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] : “Pushing arcs and graphs around in handlebodies,” pp. 163–171 in Low-dimensional topology. 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] : “Least weight injective surfaces are fundamental,” Topology Appl. 69 : 3 (April 1996), pp. 251–264. MR 1382295 Zbl 0858.57016 article

[50] : “Comparing Heegaard splittings of non-Haken 3-manifolds,” Topology 35 : 4 (October 1996), pp. 1005–1026. MR 1404921 Zbl 0858.57020 article

[51] : “Transverse Heegaard splittings,” Mich. Math. J. 44 : 1 (1997), pp. 69–83. MR 1439669 Zbl 0907.57013 article

[52] : “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] : “Comparing Heegaard splittings: The bounded case,” Trans. Am. Math. Soc. 350 : 2 (1998), pp. 689–715. MR 1401528 Zbl 0892.57009 article

[54] : “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] : “Local detection of strongly irreducible Heegaard splittings,” Topology Appl. 90 : 1–3 (December 1998), pp. 135–147. MR 1648310 Zbl 0926.57018 article

[56]
:
“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

[57] : “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

[58]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

[59] : “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

[60] : “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] : “Levelling an unknotting tunnel,” Geom. Topol. 4 (2000), pp. 243–275. MR 1778174 Zbl 0958.57007 ArXiv math/9910099 article

[62] : “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] : “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] : “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] : “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] : “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] : “Unknotting tunnels and Seifert surfaces,” Proc. London Math. Soc. (3) 87 : 2 (2003), pp. 523–544. MR 1990938 Zbl 1047.57008 ArXiv math/0010212 article

[68]
:
“Thinning genus two Heegaard spines in __\( S^3 \)__,”
J. Knot Theor. Ramif.
12 : 5
(2003),
pp. 683–708.
MR
1999638
Zbl
1048.57002
article

[69] : “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] : “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] : “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 & Topology Monographs 7. Geometry & Topology Publications (Coventry, UK), 2004. Based on the 28th University of Arkansas spring lecture series in the mathematical sciences and a conference on the topology of manifolds of dimensions 3 and 4. This paper was “Dedicated to Andrew Casson, a mathematician’s mathematician.”. MR 2172481 Zbl 1207.57016 ArXiv math/0403326 incollection

[72] : “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] : “Surfaces, submanifolds, and aligned Fox reimbedding in non-Haken 3-manifolds,” Proc. Am. Math. Soc. 133 : 6 (2005), pp. 1573–1580. MR 2120271 Zbl 1071.57015 ArXiv math/0308011 article

[74] : “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] : “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] : “Alternate Heegaard genus bounds distance,” Geom. Topol. 10 (2006), pp. 593–617. MR 2224466 Zbl 1128.57022 article

[77] : “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]
:
“Generalized property __\( R \)__ and the Schoenflies conjecture,”
Comment. Math. Helv.
83 : 2
(2008),
pp. 421–449.
MR
2390052
Zbl
1148.57032
article

[79] : “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] : “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] : “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]
:
“Surgery on a knot in (surface __\( \times I \)__),”
Algebr. Geom. Topol.
9 : 3
(2009),
pp. 1825–1835.
MR
2550096
Zbl
1197.57011
ArXiv
0807.0405
article

[84] : “A proof of the Gordon conjecture,” Adv. Math. 222 : 6 (December 2009), pp. 2085–2106. MR 2562775 Zbl 1180.57025 article

[85]
:
“Fibered knots and potential counterexamples to the property __\( 2{R} \)__ and slice-ribbon conjectures,”
Geom. Topol.
14 : 4
(2010),
pp. 2305–2347.
MR
2740649
Zbl
1214.57008
ArXiv
1103.1601
article

[86] : “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] : “Multiple genus 2 Heegaard splittings: A missed case,” Algebr. Geom. Topol. 11 : 3 (2011), pp. 1781–1792. MR 2821441 Zbl 1232.57020 article

[88] : “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]
:
“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] : 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] : “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] : Powell moves and the Goeritz group. Preprint, 2018. ArXiv 1804.05909 techreport

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

[95] : A strong Haken’s Theorem. Preprint, 2020. ArXiv 2003.08523 techreport

[96] : Uniqueness in Haken’s Theorem. Preprint, 2020. ArXiv 2004.07385 techreport