Celebratio Mathematica

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

R. Kirby: Ex­ten­sion to stable homeo­morph­isms. Single-page typescript (un­pub­lished), 1968. techreport

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

R. Kirby and L. Sieben­mann: “For man­i­folds the Hauptver­mu­tung and the tri­an­gu­la­tion con­jec­ture are false,” No­tices Amer. Math. Soc. 16 : 4 (1969), pp. 695. Ab­stract 69T-G90. article

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

D. T. Gay and R. Kirby: “In­def­in­ite Morse 2-func­tions: Broken fibra­tions and gen­er­al­iz­a­tions,” Geom. To­pol. 19 : 5 (2015), pp. 2465–​2534. MR 3416108 Zbl 1328.​57019 article

D. Gay and R. Kirby: “Tri­sect­ing 4-man­i­folds,” Geom. To­pol. 20 : 6 (2016), pp. 3097–​3132. MR 3590351 Zbl 1372.​57033 article

A. Ab­rams, D. Gay, and R. Kirby: “Group tri­sec­tions and smooth 4-man­i­folds,” Geom. To­pol. 22 : 3 (2018), pp. 1537–​1545. MR 3780440 ArXiv 1605.​06731 article