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Celebratio Mathematica

Robion C. Kirby


Bibliography

[1]R. C. Kirby: “On the an­nu­lus con­jec­ture,” Proc. Amer. Math. Soc. 17 (1966), pp. 178–​185. MR 0192481 Zbl 0151.​32902

[2]R. C. Kirby: “Smooth­ing loc­ally flat im­bed­dings,” Bull. Amer. Math. Soc. 72 (1966), pp. 147–​148. MR 0189053 Zbl 0138.​18803

[3]R. C. Kirby: “Smooth­ing loc­ally flat im­bed­dings of dif­fer­en­ti­able man­i­folds,” To­po­logy 6 (1967), pp. 207–​220. MR 0211410 Zbl 0152.​22401

[4]R. C. Kirby: “The uni­on of flat \( (n-1) \)-balls is flat in \( R^{n} \),” Bull. Amer. Math. Soc. 74 (1968), pp. 614–​617. MR 0225328 Zbl 0157.​54603

[5]R. C. Kirby: “On the set of non-loc­ally flat points of a sub­man­i­fold of codi­men­sion one,” Ann. of Math. (2) 88 (1968), pp. 281–​290. MR 0236900

[6]R. C. Kirby: “Stable homeo­morph­isms and the an­nu­lus con­jec­ture,” Ann. of Math. (2) 89 (1969), pp. 575–​582. MR 0242165 Zbl 0176.​22004

[7]R. C. Kirby and L. C. Sieben­mann: “On the tri­an­gu­la­tion of man­i­folds and the Hauptver­mu­tung,” Bull. Amer. Math. Soc. 75 (1969), pp. 742–​749. MR 0242166 Zbl 0189.​54701

[8]R. C. Kirby: “Codi­men­sion-two loc­ally flat im­bed­dings have nor­mal bundles,” pp. 416–​423 in To­po­logy of man­i­folds (Univ. of Geor­gia, Athens, GA, 1969). Markham (Chica­go, IL), 1970. MR 0273625

[9]R. C. Kirby: “Some con­jec­tures about four-man­i­folds,” pp. 79–​84 in Act­es du Con­grès In­ter­na­tion­al des Mathématiciens (Nice, 1970), tome 2. Gau­th­i­er-Vil­lars (Par­is), 1971. MR 0431179 Zbl 0223.​57004

[10]R. C. Kirby and L. C. Sieben­mann: “Some the­or­ems on to­po­lo­gic­al man­i­folds,” pp. 1–​7 in Man­i­folds–Am­s­ter­dam 1970. Lec­ture Notes in Math­em­at­ics 197. Spring­er (Ber­lin), 1971. MR 0283807 Zbl 0216.​45203

[11]R. D. Ed­wards and R. C. Kirby: “De­form­a­tions of spaces of im­bed­dings,” Ann. Math. (2) 93 (1971), pp. 63–​88. MR 0283802 Zbl 0214.​50303

[12]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

[13]R. C. Kirby and L. C. Sieben­mann: “Nor­mal bundles for codi­men­sion-2 loc­ally flat im­bed­dings,” pp. 310–​324 in Geo­met­ric to­po­logy (Park City, UT, 1974). Edi­ted by L. C. Glaser and T. B. Rush­ing. Lec­ture Notes in Math. 438. Spring­er (Ber­lin), 1975. MR 0400237 Zbl 0331.​57004

[14]R. C. Kirby and L. C. Sieben­mann: Found­a­tion­al es­says on to­po­lo­gic­al man­i­folds, smooth­ings, and tri­an­gu­la­tions. An­nals of Math­em­at­ics Stud­ies 88. Prin­ceton Uni­versity Press, 1977. With notes by John Mil­nor and Mi­chael Atiyah. MR 0645390 Zbl 0361.​57004 book

[15] incollection M. Freed­man and R. Kirby: “A geo­met­ric proof of Roch­lin’s the­or­em,” pp. 85–​97 in Al­geb­ra­ic and geo­met­ric to­po­logy (Stan­ford Uni­versity, CA, Au­gust 2–21, 1976), part 2. Edi­ted by R. J. Mil­gram. Pro­ceed­ings of Sym­po­sia in Pure Math­em­at­ics XXXII. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1978. MR 0520525 Zbl 0392.​57018

[16]R. Kirby: “A cal­cu­lus for framed links in \( S^{3} \),” In­vent. Math. 45 : 1 (1978), pp. 35–​56. MR 0467753 Zbl 0377.​55001

[17]R. Kirby and P. Melvin: “Slice knots and prop­erty R,” In­vent. Math. 45 : 1 (1978), pp. 57–​59. MR 0467754 Zbl 0377.​55002

[18]R. Kirby: “Prob­lems in low di­men­sion­al man­i­fold the­ory,” pp. 273–​312 in Al­geb­ra­ic and geo­met­ric to­po­logy (Stan­ford Univ., CA, 1976), part 2. Edi­ted by R. J. Mil­gram. Proc. Sym­pos. Pure Math. XXXII. Amer. Math. Soc. (Provid­ence, R.I.), 1978. MR 520548 Zbl 0394.​57002

[19]S. Ak­bu­lut and R. Kirby: “Mazur man­i­folds,” Michigan Math. J. 26 : 3 (1979), pp. 259–​284. MR 544597 Zbl 0443.​57011

[20]S. Ak­bu­lut and R. Kirby: “An exot­ic in­vol­u­tion of \( S^{4} \),” To­po­logy 18 : 1 (1979), pp. 75–​81. MR 528237 Zbl 0465.​57013

[21]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

[22]R. C. Kirby and W. B. R. Lick­or­ish: “Prime knots and con­cord­ance,” Math. Proc. Cam­bridge Philos. Soc. 86 : 3 (1979), pp. 437–​441. MR 542689 Zbl 0426.​57001

[23]S. Ak­bu­lut and R. Kirby: “Branched cov­ers of sur­faces in 4-man­i­folds,” Math. Ann. 252 : 2 (1979/80), pp. 111–​131. MR 593626 Zbl 0421.​57002

[24]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

[25]R. Kirby: “4-man­i­fold prob­lems,” pp. 513–​528 in Four-man­i­fold the­ory (Durham, NH, 1982). Edi­ted by C. Gor­don and R. Kirby. Con­temp. Math. 35. Amer. Math. Soc. (Provid­ence, RI), 1984. MR 780598

[26]Four-man­i­fold the­ory (Durham, NH, Ju­ly 4–10, 1982). Edi­ted by C. Gor­don and R. Kirby. Con­tem­por­ary Math­em­at­ics 35. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1984. MR 780574

[27]S. Ak­bu­lut and R. Kirby: “A po­ten­tial smooth counter­example in di­men­sion 4 to the Poin­caré con­jec­ture, the Schoen­flies con­jec­ture, and the An­drews–Curtis con­jec­ture,” To­po­logy 24 : 4 (1985), pp. 375–​390. MR 816520 Zbl 0584.​57009

[28]J. Harer, A. Kas, and R. Kirby: “Handle­body de­com­pos­i­tions of com­plex sur­faces,” Mem. Amer. Math. Soc. 62 : 350 (1986), pp. iv+102. MR 849942

[29]R. C. Kirby: The to­po­logy of 4-man­i­folds. Lec­ture Notes in Math­em­at­ics 1374. Spring­er (Ber­lin), 1989. MR 1001966 Zbl 0668.​57001

[30]R. Kirby and P. Melvin: “Eval­u­ations of the 3-man­i­fold in­vari­ants of Wit­ten and Resh­et­ikh­in–Tur­aev for \( \mathrm{sl}(2,\mathbf{C}) \),” pp. 101–​114 in Geo­metry of low-di­men­sion­al man­i­folds (Durham, 1989), vol. 2. Edi­ted by S. K. Don­ald­son and C. B. Thomas. Lon­don Math. Soc. Lec­ture Note Ser. 151. Cam­bridge Univ. Press, 1990. MR 1171911 Zbl 0756.​57006

[31]R. C. Kirby and L. R. Taylor: “\( \mathit{Pin} \) struc­tures on low-di­men­sion­al man­i­folds,” pp. 177–​242 in Geo­metry of low-di­men­sion­al man­i­folds (Durham, 1989), vol. 2. Edi­ted by S. K. Don­ald­son and C. B. Thomas. Lon­don Math. Soc. Lec­ture Note Ser. 151. Cam­bridge Univ. Press, 1990. MR 1171915 Zbl 0754.​57020

[32]R. C. Kirby and L. R. Taylor: “A cal­cu­la­tion of \( \mathrm{Pin}^+ \) bor­d­ism groups,” Com­ment. Math. Helv. 65 : 3 (1990), pp. 434–​447. MR 1069818 Zbl 0719.​55004

[33]R. Kirby and P. Melvin: “The 3-man­i­fold in­vari­ants of Wit­ten and Resh­et­ikh­in–Tur­aev for \( \mathrm{sl}(2,\mathbf{C}) \),” In­vent. Math. 105 : 3 (1991), pp. 473–​545. MR 1117149 Zbl 0745.​57006

[34]R. Kirby, P. Melvin, and X. Zhang: “Quantum in­vari­ants at the sixth root of unity,” Comm. Math. Phys. 151 : 3 (1993), pp. 607–​617. MR 1207268 Zbl 0779.​57007

[35]R. Kirby and P. Melvin: “Dede­kind sums, \( \mu \)-in­vari­ants and the sig­na­ture cocycle,” Math. Ann. 299 : 2 (1994), pp. 231–​267. MR 1275766 Zbl 0809.​11027

[36]R. Kirby: “Ak­bu­lut’s corks and \( h \)-cobor­d­isms of smooth, simply con­nec­ted 4-man­i­folds,” Turk­ish J. Math. 20 : 1 (1996), pp. 85–​93. MR 1392665 Zbl 0868.​57031

[37]R. Kirby: “Prob­lems in low-di­men­sion­al to­po­logy,” pp. 35–​473 in Geo­met­ric to­po­logy (Athens, GA, 1993). Edi­ted by W. H. Kazez. AMS/IP Stud. Adv. Math. 2. Amer. Math. Soc. (Provid­ence, RI), 1997. MR 1470751

[38]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

[39]R. Kirby and P. Melvin: “Ca­non­ic­al fram­ings for 3-man­i­folds,” pp. 89–​115 in Pro­ceed­ings of 6th Gökova Geo­metry-To­po­logy Con­fer­ence, published as Turk­ish J. Math. 23 : 1. 1999. MR 1701641 Zbl 0947.​57020

[40]R. Kirby and P. Melvin: “The \( E_8 \)-man­i­fold, sin­gu­lar fibers and handle­body de­com­pos­i­tions,” pp. 233–​258 in Pro­ceed­ings of the Kirby­fest (Berke­ley, CA, 1998). Edi­ted by J. Hass and M. Schar­le­mann. Geom. To­pol. Mono­gr. 2. Geom. To­pol. Publ., Cov­entry, 1999. MR 1734411 Zbl 0959.​57020

[41]R. C. Kirby and L. R. Taylor: “A sur­vey of 4-man­i­folds through the eyes of sur­gery,” pp. 387–​421 in Sur­veys on sur­gery the­ory: Pa­pers ded­ic­ated to C. T. C. Wall, vol. 2. Edi­ted by S. Cap­pell, A. Ran­icki, and J. Rosen­berg. Ann. of Math. Stud. 149. Prin­ceton Univ. Press, 2001. MR 1818779 Zbl 0974.​57012

[42]R. Kirby: “Con­ver­sa­tions about math­em­at­ics,” No­tices Amer. Math. Soc. 49 : 3 (2002), pp. 333–​335. MR 1879859 Zbl 1126.​00302

[43]D. T. Gay and R. Kirby: “Con­struct­ing sym­plect­ic forms on 4-man­i­folds which van­ish on circles,” Geom. To­pol. 8 (2004), pp. 743–​777. MR 2057780 Zbl 1054.​57027

[44]R. Kirby and P. Melvin: “Loc­al sur­gery for­mu­las for quantum in­vari­ants and the Arf in­vari­ant,” pp. 213–​233 in Pro­ceed­ings of the Cas­son Fest. Edi­ted by C. Gor­don and Y. Rieck. Geom. To­pol. Mono­gr. 7. Geom. To­pol. Publ. (Cov­entry), 2004. MR 2172485 Zbl 1087.​57006

[45]D. T. Gay and R. Kirby: “Con­struct­ing Lef­schetz-type fibra­tions on four-man­i­folds,” Geom. To­pol. 11 (2007), pp. 2075–​2115. MR 2350472 Zbl 1135.​57009

[46]D. T. Gay and R. C. Kirby: “Fiber-con­nec­ted, in­def­in­ite Morse 2-func­tions on con­nec­ted \( n \)-man­i­folds,” Proc. Natl. Acad. Sci. USA 108 : 20 (2011), pp. 8122–​8125. MR 2806648

[47]R. C. Kirby: “Low-di­men­sion­al to­po­logy and geo­metry,” Proc. Natl. Acad. Sci. USA 108 : 20 (2011), pp. 8081–​8084. MR 2806642