Celebratio Mathematica

Michael F. Atiyah

Papers on K-theory (1959–1970)

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M. F. Atiyah and F. Hirzebruch: “Riemann–Roch the­or­ems for dif­fer­en­ti­able man­i­folds,” Bull. Amer. Math. Soc. 65 : 4 (1959), pp. 276–​281. MR 0110106 Zbl 0142.​40901 article

M. F. Atiyah and F. Hirzebruch: “Quelques théorèmes de non-plonge­ment pour les var­iétés différen­ti­ables” [Some the­or­ems of non-im­mer­sion for dif­fer­en­ti­able man­i­folds], Bull. Soc. Math. France 87 (1959), pp. 383–​396. See also Col­loques Int. Centre Nat. Rech. Sci. 89 (1960). MR 0114231 article

M. F. Atiyah and J. A. Todd: “On com­plex Stiefel man­i­folds,” Proc. Cam­bridge Philos. Soc. 56 : 4 (1960), pp. 342–​353. MR 0132552 Zbl 0109.​16102 article

M. F. Atiyah and F. Hirzebruch: “Quelques théoremes de non-plonge­ment pour les var­iétés différen­ti­ables” [Some non-em­bed­ding the­or­ems for dif­fer­en­ti­able man­i­folds], Col­loques Int. Centre Nat. Rech. Sci. 89 (1960), pp. 383–​396. See also Bull. Soc. Math. France 87 (1959). Zbl 0108.​18202 article

M. F. Atiyah and F. Hirzebruch: “Vec­tor bundles and ho­mo­gen­eous spaces,” pp. 7–​38 in Dif­fer­en­tial geo­metry. Edi­ted by C. B. Al­lendo­er­fer. Pro­ceed­ings of Sym­po­sia in Pure Math­em­at­ics 3. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1961. MR 0139181 Zbl 0108.​17705 incollection

M. F. Atiyah: “Char­ac­ters and co­homo­logy of fi­nite groups,” Inst. Hautes Études Sci. Publ. Math. 9 : 1 (1961), pp. 23–​64. MR 0148722 Zbl 0107.​02303 article

M. F. Atiyah: “Thom com­plexes,” Proc. Lon­don Math. Soc. (3) 11 : 1 (1961), pp. 291–​310. MR 0131880 Zbl 0124.​16301 article

M. F. Atiyah and F. Hirzebruch: “Co­homo­lo­gie-Op­er­a­tion­en und charak­ter­istische Klassen,” Math. Z. 77 : 1 (1961), pp. 149–​187. MR 0156361 Zbl 0109.​16002 article

M. F. Atiyah: “Bor­d­ism and cobor­d­ism,” Proc. Cam­bridge Philos. Soc. 57 (1961), pp. 200–​208. MR 0126856 Zbl 0104.​17405 article

M. F. Atiyah and F. Hirzebruch: “Bott peri­od­icity and the par­al­lel­iz­ab­il­ity of the spheres,” Proc. Cam­bridge Philos. Soc. 57 (1961), pp. 223–​226. MR 0126282 Zbl 0108.​35902 article

M. F. Atiyah and F. Hirzebruch: “Charak­ter­istische Klassen und An­wendun­gen,” En­sei­gne­ment Math. (2) 7 (1961), pp. 188–​213. MR 0154294 Zbl 0104.​39801 article

M. F. Atiyah and F. Hirzebruch: “The Riemann–Roch the­or­em for ana­lyt­ic em­bed­dings,” To­po­logy 1 : 2 (1962), pp. 151–​166. MR 0148084 Zbl 0108.​36402 article

M. F. Atiyah: “Vec­tor bundles and the Kün­neth for­mula,” To­po­logy 1 : 3 (1962), pp. 245–​248. MR 0150780 article

M. F. Atiyah and F. Hirzebruch: “Ana­lyt­ic cycles on com­plex man­i­folds,” To­po­logy 1 (1962), pp. 25–​45. MR 0145560 Zbl 0108.​36401 article

M. F. Atiyah: “Im­mer­sions and em­bed­dings of man­i­folds,” To­po­logy 1 : 2 (April–June 1962), pp. 125–​132. MR 0145549 Zbl 0109.​41101 article

M. F. Atiyah: “The Grothen­dieck ring in geo­metry and to­po­logy,” pp. 442–​446 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians 1962 (Stock­holm, 15–22 Au­gust 1962), vol. 1. Inst. Mit­tag-Leffler (Djur­sholm), 1963. MR 0180975 Zbl 0121.​39702 incollection

M. F. Atiyah, R. Bott, and A. Sha­piro: “Clif­ford mod­ules,” To­po­logy 3 : Supplement 1 (July 1964), pp. 3–​38. MR 0167985 Zbl 0146.​19001 article

M. Atiyah and R. Bott: “On the peri­od­icity the­or­em for com­plex vec­tor bundles,” Acta Math. 112 : 1 (1964), pp. 229–​247. MR 0178470 Zbl 0131.​38201 article

M. F. Atiyah: “On the \( K \)-the­ory of com­pact Lie groups,” To­po­logy 4 : 1 (1965), pp. 95–​99. MR 0178092 Zbl 0136.​21001 article

M. F. Atiyah: “\( K \)-the­ory and real­ity,” Quart. J. Math. Ox­ford Ser. (2) 17 : 1 (1966), pp. 367–​386. MR 0206940 Zbl 0146.​19101 article

J. F. Adams and M. F. Atiyah: “\( K \)-the­ory and the Hopf in­vari­ant,” Quart. J. Math. Ox­ford Ser. (2) 17 (1966), pp. 31–​38. MR 0198460 Zbl 0136.​43903 article

M. F. Atiyah: “Power op­er­a­tions in \( K \)-the­ory,” Quart. J. Math. Ox­ford Ser. (2) 17 : 1 (1966), pp. 165–​193. Rus­si­an trans­la­tion pub­lished in Math­em­atika 14:2 (1970). MR 0202130 Zbl 0144.​44901 article

M. F. Atiyah and D. W. An­der­son: \( K \)-the­ory. Math­em­at­ics Lec­ture Notes 7. W. A. Ben­jamin (New York and Am­s­ter­dam), 1967. Lec­tures by Atiyah (Fall 1964), notes by An­der­son. Rus­si­an trans­la­tion pub­lished as Lekcii po \( K \)-teorii (1967). 2nd edi­tion pub­lished in 1989. MR 0224083 book

M. F. Atiyah and D. W. An­der­son: Lekcii po \( K \)-teorii [Lec­tures on \( K \)-the­ory]. Mir (Mo­scow), 1967. Rus­si­an trans­la­tion of \( K \)-the­ory (1967). Zbl 0159.​53401 book

M. F. Atiyah: “Bott peri­od­icity and the in­dex of el­lipt­ic op­er­at­ors,” Quart. J. Math. Ox­ford Ser. (2) 19 (1968), pp. 113–​140. MR 0228000 Zbl 0159.​53501 article

M. F. Atiyah: “Al­geb­ra­ic to­po­logy and op­er­at­ors in Hil­bert space,” pp. 101–​121 in Lec­tures in mod­ern ana­lys­is and ap­plic­a­tions, vol. I. Edi­ted by C. T. Taam. Lec­ture Notes in Math­em­at­ics 103. Spring­er (Ber­lin), 1969. MR 0248803 Zbl 0177.​51701 incollection

M. F. Atiyah and G. B. Segal: “Equivari­ant \( K \)-the­ory and com­ple­tion,” J. Dif­fer­en­tial Geo­metry 3 (1969), pp. 1–​18. MR 0259946 Zbl 0215.​24403 article

M. F. Atiyah and D. O. Tall: “Group rep­res­ent­a­tions, \( \lambda \)-rings and the \( J \)-ho­mo­morph­ism,” To­po­logy 8 : 3 (July 1969), pp. 253–​297. MR 0244387 Zbl 0159.​53301 article

M. F. Atiyah: Vec­tor fields on man­i­folds. Arbeits­ge­meinsch­aft für Forschung des Landes Nordrhein-West­falen 200. West­deutscher Ver­lag (Co­logne), 1970. MR 0263102 Zbl 0193.​52303 book

M. F. Atiyah: “Power op­er­a­tions in \( K \)-the­ory,” Matem­atika 14 : 2 (1970), pp. 35–​65. Rus­si­an trans­la­tion of art­icle in Q. J. Math., Oxf. 17:1 (1966). Zbl 0208.​51503 article

M. F. Atiyah: “El­lipt­ic op­er­at­ors and sin­gu­lar­it­ies of vec­tor fields,” pp. 207–​209 in Act­es du Con­grès In­ter­na­tion­al des Math­ématiciens (Nice, 1–10 Septem­ber 1970), vol. 2. Gau­th­i­er-Vil­lars (Par­is), 1971. MR 0415688 Zbl 0222.​58004 incollection

M. F. Atiyah and G. B. Segal: “Ex­po­nen­tial iso­morph­isms for \( \lambda \)-rings,” Quart. J. Math. Ox­ford Ser. (2) 22 : 3 (1971), pp. 371–​378. MR 0291250 Zbl 0226.​13008 article

M. F. Atiyah and J. L. Dupont: “Vec­tor fields with fi­nite sin­gu­lar­it­ies,” Acta Math. 128 : 1 (1972), pp. 1–​40. MR 0451256 Zbl 0233.​57010 article

M. F. Atiyah and L. Smith: “Com­pact Lie groups and the stable ho­mo­topy of spheres,” To­po­logy 13 : 2 (1974), pp. 135–​142. MR 0343269 Zbl 0282.​55008 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. Atiyah: Col­lec­ted works, vol. 2: \( K \)-the­ory. Ox­ford Sci­ence Pub­lic­a­tions. The Clar­en­don Press and Ox­ford Uni­versity Press (Ox­ford and New York), 1988. MR 951893 Zbl 0724.​55001 book

M. F. Atiyah and D. W. An­der­son: \( K \)-the­ory, 2nd edition. Ad­vanced Book Clas­sics. Ad­dis­on-Wes­ley (Red­wood City, CA), 1989. Ori­gin­al edi­tion pub­lished by W. A. Ben­jamin in 1967. MR 1043170 book