Celebratio Mathematica

Michael F. Atiyah

Geometry

Works of Michael Atiyah

Works connected to Isadore M. Singer

Filter the Bibliography List

clear

M. F. Atiyah and I. M. Sing­er: “The in­dex of el­lipt­ic op­er­at­ors on com­pact man­i­folds,” Bull. Amer. Math. Soc. 69 (1963), pp. 422–​433. Re­prin­ted in Sémin­aire Bourbaki. 15e an­née: 1962/63 (1964) and Sémin­aire Bourbaki 8 (1995). MR 0157392 Zbl 0118.​31203 article

M. F. Atiyah and I. M. Sing­er: “The in­dex of el­lipt­ic op­er­at­ors, I,” Ann. Math. (2) 87 : 3 (1968), pp. 484–​530. Rus­si­an trans­la­tion pub­lished in Usp. Mat. Nauk 23:5(143) (1968). MR 0236950 Zbl 0164.​24001 article

M. F. Atiyah and I. M. Sing­er: “The in­dex of el­lipt­ic op­er­at­ors, III,” Ann. Math. (2) 87 : 3 (1968), pp. 546–​604. Rus­si­an trans­la­tion pub­lished in Us­pehi Mat. Nauk 24:1(145) (1969). MR 0236952 Zbl 0164.​24301 article

M. F. Atiyah and I. M. Sing­er: “The in­dex of el­lipt­ic op­er­at­ors, I,” Us­pehi Mat. Nauk 23 : 5 (143) (1968), pp. 99–​142. Rus­si­an trans­la­tion of art­icle from Ann. Math. 87:3 (1968). MR 0232402 article

M. F. Atiyah and I. M. Sing­er: “In­dex the­ory for skew-ad­joint Fred­holm op­er­at­ors,” Inst. Hautes Études Sci. Publ. Math. 37 : 1 (January 1969), pp. 5–​26. MR 0285033 Zbl 0194.​55503 article

M. F. Atiyah and I. M. Sing­er: “The in­dex of el­lipt­ic op­er­at­ors, III,” Us­pehi Mat. Nauk 24 : 1 (145) (1969), pp. 127–​182. Rus­si­an trans­la­tion of art­icle in Ann. Math. 87:3 (1968). MR 0256417 article

M. F. Atiyah and I. M. Sing­er: “The in­dex of el­lipt­ic op­er­at­ors, V,” Ann. Math. (2) 93 : 1 (1971), pp. 139–​149. Rus­si­an trans­la­tion pub­lished in Us­pehi Mat. Nauk 27:4(166) (1972). MR 0279834 article

M. F. Atiyah and I. M. Sing­er: “The in­dex of el­lipt­ic op­er­at­ors, IV,” Ann. Math. (2) 93 : 1 (1971), pp. 119–​138. Rus­si­an trans­la­tion pub­lished in Us­pehi Mat. Nauk 27:4(166) (1972). MR 0279833 article

M. F. Atiyah and I. M. Sing­er: “The in­dex of el­lipt­ic op­er­at­ors, IV,” Us­pehi Mat. Nauk 27 : 4(166) (1972), pp. 161–​178. Rus­si­an trans­la­tion of Ann. Math. 93:1 (1971). MR 0385933 article

M. F. Atiyah and I. M. Sing­er: “The in­dex of el­lipt­ic op­er­at­ors, V,” Usp. Mat. Nauk 27 : 4(166) (1972), pp. 179–​188. Rus­si­an trans­la­tion of Ann. Math. 93:1 (1971). Zbl 0237.​58018 article

M. F. Atiyah, V. K. Pat­odi, and I. M. Sing­er: “Spec­tral asym­metry and Rieman­ni­an geo­metry,” Bull. Lon­don Math. Soc. 5 : 2 (1973), pp. 229–​234. MR 0331443 Zbl 0268.​58010 article

M. F. Atiyah, V. K. Pat­odi, and I. M. Sing­er: “Spec­tral asym­metry and Rieman­ni­an geo­metry, II,” Math. Proc. Cam­bridge Philos. Soc. 78 : 3 (1975), pp. 405–​432. MR 0397798 Zbl 0314.​58016 article

M. F. Atiyah, V. K. Pat­odi, and I. M. Sing­er: “Spec­tral asym­metry and Rieman­ni­an geo­metry, I,” Math. Proc. Cam­bridge Philos. Soc. 77 : 1 (1975), pp. 43–​69. MR 0397797 Zbl 0297.​58008 article

M. F. Atiyah, V. K. Pat­odi, and I. M. Sing­er: “Spec­tral asym­metry and Rieman­ni­an geo­metry, III,” Math. Proc. Cam­bridge Philos. Soc. 79 : 1 (1976), pp. 71–​99. MR 0397799 Zbl 0325.​58015 article

M. F. Atiyah, N. J. Hitchin, and I. M. Sing­er: “De­form­a­tions of in­stan­tons,” Proc. Nat. Acad. Sci. U.S.A. 74 : 7 (1977), pp. 2662–​2663. MR 0458424 Zbl 0356.​58011 article

M. F. Atiyah: “A sur­vey of \( K \)-the­ory,” pp. 1–​9 in \( K \)-the­ory and op­er­at­or al­geb­ras (Uni­versity of Geor­gia, Athens, GA, 21–25 April 1975). Edi­ted by B. B. Mor­rel and I. M. Sing­er. Spring­er (Ber­lin), 1977. MR 0474299 Zbl 0345.​55005 incollection

M. F. Atiyah, N. J. Hitchin, and I. M. Sing­er: “Self-du­al­ity in four-di­men­sion­al Rieman­ni­an geo­metry,” Proc. Roy. Soc. Lon­don Ser. A 362 : 1711 (1978), pp. 425–​461. MR 506229 Zbl 0389.​53011 article

M. F. Atiyah: “Re­marks on Morse the­ory,” pp. 1–​5 in Re­cent de­vel­op­ments in gauge the­or­ies. Edi­ted by G. ’t Hooft, C. Itzyk­son, A. Jaffe, H. Lehmann, P. K. Mit­ter, I. M. Sing­er, and R. Stora. NATO Ad­vanced Study In­sti­tutes Series B. Phys­ics. 59. Plen­um Press (New York and Lon­don), 1980. Re­pub­lished in Atiyah’s Col­lec­ted works, vol. 5. incollection

M. F. Atiyah, H. Don­nelly, and I. M. Sing­er: “Geo­metry and ana­lys­is of Shim­izu \( L \)-func­tions,” Proc. Nat. Acad. Sci. U.S.A. 79 : 18 (1982), pp. 5751. MR 674920 Zbl 0503.​12007 article

M. F. Atiyah, H. Don­nelly, and I. M. Sing­er: “Eta in­vari­ants, sig­na­ture de­fects of cusps, and val­ues of \( L \)-func­tions,” Ann. Math. (2) 118 : 1 (1983), pp. 131–​177. An ad­dendum was pub­lished in Ann. Math. 119:3 (1984). MR 707164 Zbl 0531.​58048 article

M. F. Atiyah and I. M. Sing­er: “Dir­ac op­er­at­ors coupled to vec­tor po­ten­tials,” Proc. Nat. Acad. Sci. U.S.A. 81 : 8 (1984), pp. 2597–​2600. MR 742394 Zbl 0547.​58033 article

M. F. Atiyah, H. Don­nelly, and I. M. Sing­er: “Sig­na­ture de­fects of cusps and val­ues of \( L \)-func­tions: The non­split case. Ad­dendum to: ‘Eta in­vari­ants, sig­na­ture de­fects of cusps, and val­ues of \( L \)-func­tions’,” Ann. Math. (2) 119 : 3 (1984), pp. 635–​637. Ad­dendum to an art­icle in Ann. Math. 118:1 (1983). MR 744866 article

Pa­pers ded­ic­ated to Atiyah, Bott, Hirzebruch, and Sing­er. Edi­ted by S.-T. Yau. Sur­veys in Dif­fer­en­tial Geo­metry (sup­ple­ment to Journ­al of Dif­fer­en­tial Geo­metry) 7. In­ter­na­tion­al Press (Somerville, MA), 2000. MR 1919419 book

The founders of in­dex the­ory: Re­min­is­cences of Atiyah, Bott, Hirzebruch, and Sing­er. Edi­ted by S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2003. 2nd edi­tion was pub­lished in 2009. MR 2136846 Zbl 1072.​01021 book

E. Wit­ten: “Mi­chael Atiyah and the phys­ics/geo­metry in­ter­face,” pp. 43–​50 in The founders of in­dex the­ory: Re­min­is­cences of and about Sir Mi­chael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Sing­er. Edi­ted by S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2003. Re­pub­lished from Asi­an J. Math. 3:1 (1999). Also in the 2009 edi­tion of the book. incollection

N. Hitchin: “Sir Mi­chael Atiyah: A brief bio­graphy,” pp. 15–​22 in The founders of in­dex the­ory: Re­min­is­cences of and about Sir Mi­chael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Sing­er. Edi­ted by S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2003. Also in the 2009 edi­tion of the book. incollection

M. Atiyah: “The con­science of sci­ence,” pp. 51–​66 in The founders of in­dex the­ory: Re­min­is­cences of and about Sir Mi­chael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Sing­er. Edi­ted by S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2003. Also in the 2009 edi­tion of the book. incollection

G. Lusztig: “Re­col­lec­tions about my teach­er Mi­chael Atiyah,” pp. 37–​42 in The founders of in­dex the­ory: Re­min­is­cences of and about Sir Mi­chael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Sing­er. Edi­ted by S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2003. Re­pub­lished from Asi­an J. Math. 3:1 (1999). Also in the 2009 edi­tion of the book. incollection

P. God­dard: “Sir Mi­chael Atiyah and the early days of the New­ton In­sti­tute,” pp. 23–​28 in The founders of in­dex the­ory: Re­min­is­cences of and about Sir Mi­chael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Sing­er. Edi­ted by S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2003. Also in the 2009 edi­tion of the book. incollection

In­ter­view with Mi­chael Atiyah and Is­ad­ore Sing­er,” Mitt. Dtsch. Math.-Ver. 12 : 4 (2004), pp. 272–​281. Re­pub­lished from Eur. Math. Soc. Newsl. (Septem­ber 2004). See also No­tices Amer. Math. Soc. 52:2 (2005). MR 2110686 article

Norwegian Academy of Science and Letters: “Atiyah and Sing­er re­ceive 2004 Abel Prize,” No­tices Amer. Math. Soc. 51 : 6 (2004), pp. 649–​650. Press re­lease. MR 2064152 article

In­ter­view with Mi­chael Atiyah and Is­ad­ore Sing­er,” Eur. Math. Soc. Newsl. (September 2004), pp. 24–​30. Re­pub­lished in No­tices Amer. Math. Soc. 52:2 (2005) and Mitt. Dtsch. Math.-Ver. 12:4 (2004). article

M. Raussen and C. Skau: “In­ter­view with Mi­chael Atiyah and Is­ad­ore Sing­er,” No­tices Amer. Math. Soc. 52 : 2 (2005), pp. 225–​233. Re­pub­lished from Eur. Math. Soc. Newsl. (Septem­ber 2004). See also Mitt. Dtsch. Math.-Ver. 12:4 (2004). MR 2110633 Zbl 1142.​01347 article

M. Atiyah: “The in­ter­ac­tion between geo­metry and phys­ics,” pp. 1–​15 in The unity of math­em­at­ics (Cam­bridge, MA, 31 Au­gust–4 Septem­ber 2003). Edi­ted by P. I. Ètin­gof, V. Re­takh, and I. M. Sing­er. Pro­gress in Math­em­at­ics 244. Birkhäuser (Bo­ston, MA), 2006. MR 2181802 Zbl 1118.​58002 incollection

The founders of in­dex the­ory: Re­min­is­cences of Atiyah, Bott, Hirzebruch, and Sing­er, 2nd edition. Edi­ted by S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2009. Ori­gin­al edi­tion was pub­lished in 2003. MR 2547480 Zbl 1195.​01090 book

M. F. Atiyah: “A per­son­al his­tory,” pp. 5–​15 in The founders of in­dex the­ory: Re­min­is­cences of and about Sir Mi­chael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Sing­er, 2nd edition. Edi­ted by S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2009. Re­pub­lished in Atiyah’s Col­lec­ted works, vol. 6. incollection

S. Don­ald­son: “Geo­metry in Ox­ford c.1980–85,” pp. 35–​42 in The founders of in­dex the­ory: Re­min­is­cences of and about Sir Mi­chael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Sing­er, 2nd edition. Edi­ted by S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2009. Re­pub­lished from Asi­an J. Math. 3:1 (1999). Also in the 2003 edi­tion of the book. incollection

L. Niren­berg: “Memor­ies of Mi­chael Atiyah,” pp. 45–​46 in The founders of in­dex the­ory: Re­min­is­cences of and about Sir Mi­chael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Sing­er, 2nd edition. Edi­ted by S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2009. incollection

M. Atiyah: “Memor­ies of Raoul Bott,” pp. 89–​94 in The founders of in­dex the­ory: Re­min­is­cences of Atiyah, Bott, Hirzebruch, and Sing­er. Edi­ted by S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2009. incollection

M. Atiyah: “Let­ter to Raoul, Fritz, and Is,” pp. 323–​324 in The founders of in­dex the­ory: Re­min­is­cences of and about Sir Mi­chael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Sing­er, 2nd edition. Edi­ted by S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2009. Also found in the 2003 edi­tion of the book. incollection

R. Bott: “A let­ter from Raoul Bott,” pp. 33–​34 in The founders of in­dex the­ory: Re­min­is­cences of and about Sir Mi­chael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Sing­er, 2nd edition. Edi­ted by S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2009. Also in the 2003 edi­tion of the book. incollection

G. Segal: “Be­ing a gradu­ate stu­dent of Mi­chael Atiyah,” pp. 47–​48 in The founders of in­dex the­ory: Re­min­is­cences of and about Sir Mi­chael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Sing­er, 2nd edition. Edi­ted by S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2009. Also in the 2003 edi­tion of the book. incollection

M. Atiyah: “Math­em­at­ics: Queen and ser­vant of the sci­ences,” pp. 55–​76 in The founders of in­dex the­ory: Re­min­is­cences of and about Sir Mi­chael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Sing­er, 2nd edition. Edi­ted by S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2009. Re­pub­lished from Proc. Am. Phil. Soc. 137:4 (1993). See also Asi­an J. Math. 3:1 (1999). incollection

D. Burns, L. Ji, K. Liu, A. Ran­icki, and S.-T. Yau: “Pre­face,” pp. 1–​3 in Spe­cial is­sue: In hon­or of Mi­chael Atiyah and Is­ad­ore Sing­er, published as Pure Ap­pl. Math. Q. 6 : 2 (2010). MR 2761847 incollection

Spe­cial is­sue: In hon­or of Mi­chael Atiyah and Is­ad­ore Sing­er, published as Pure Ap­pl. Math. Q. 6 : 2 (2010). book