Signature modulo 16, invariants de Kervaire généralisés et nombres caractéristiques dans la K-théorie réelle (1981)


Ochanine, S.
Mémoires de la Société Mathématique de France, Tome 5 (1981) 156 p doi : 10.24033/msmf.290
URL stable : http://www.numdam.org/item?id=MSMF_1981_2_5__1_0

Bibliographie

[1] Adams J.F., On the groups J(X) - IV, Topology, 5, 1966, 21-27. MR 33 #6628 | Zbl 0145.19902

[2] Anderson D. W., Brown E.H., Peterson F. P., SU-cobordism, KO-characteristic numbers, and the Kervaire invariant, Ann. Math., 83, 1966, 54-67. MR 32 #6470 | Zbl 0137.42802

[3] Anderson D. W., Brown E. H., Peterson F. P., The structure of the Spin cobordism ring, Ann. Math., 86, 1967, 271-298. MR 36 #2160 | Zbl 0156.21605

[4] Anderson P. G., Cobordism classes of squares of orientable manifolds, Ann. Math., 83, 1966, 47-53. MR 32 #4700 | Zbl 0134.42704

[5] Atiyah M. F., Bott R., Shapiro A., Clifford modules, Topology, 3, 1964, Suppl. 1, 3-38. MR 29 #5250 | Zbl 0146.19001

[6] Atiyah M. F., Singer I. M., The index of elliptic operators: III, Ann. Math., 87, 1968, 546-604. MR 38 #5245 | Zbl 0164.24301

[7] Atiyah M. F., Macdonald I. G., Introduction to commutative algebra, Addison-Wesley, Reading, Massachusetts, 1969. MR 39 #4129 | Zbl 0175.03601

[8] Borel A., La cohomologie mod 2 de certains espaces homogènes, Comment. Math. Helv., 27, 1953, 165-197. MR 15,244h | Zbl 0052.40301

[9] Borel A., Hirzebruch F., Characteristic classes and homogeneous spaces, III, Amer. J. Math., 82, 1960, 491-504. MR 22 #11413 | Zbl 0097.36401

[10] Бopebич З.И., Шaфapebич И.P., TeopиЯ ЧиceЛ "Hayka", Mockba, 1972.

[10*] Borevich Z. I., Shafarevich I.R., Number theory, Acad. Press, New-York, 1966. Zbl 0145.04902

[11] Browder W., The Kervaire invariant of framed manifolds and its generalisations, Ann. Math., 90, 1969, 157-186. MR 40 #4963 | Zbl 0198.28501

[12] Browder W., Surgery on simply-connected manifolds, Ergebnisse der Math., Band 65, Springer-Verlag, Berlin, Heidelberg, New-York, 1972. MR 50 #11272 | Zbl 0239.57016

[13] Browder W., Complete intersections and the Kervaire invariant, Lecture Notes Math., 763, 1979, 88-108. MR 81i:57019 | Zbl 0429.57010

[14] Brown E. H., Note on an invariant of Kervaire, Mich. Math. J., 12, 1965, 23-24. MR 32 #8351 | Zbl 0129.39002

[15] Brown E.H., Peterson F.P., The Kervaire invariant of (8k+2)-manifolds, Amer. J. Math., 88, 1966, 815-826. MR 34 #6786 | Zbl 0148.17401

[16] Brown E.H., Generalizations of the Kervaire invariant, Ann. Math., 95, 1972, 368-383. MR 45 #2719 | Zbl 0241.57014

[17] Brown E.H., A product formula for an Arf-Kervaire invariant, Bull. Amer. Math. Soc., 80, 1974, 873-874. MR 50 #8561 | Zbl 0292.57006

[18] Буxштабер B.M./Buchstaber/, Проекторы в унитарныx кобордиӡмаx, свяӡанные с SU-теорией /Projecteurs en cobordismes complexes liés à la SU-théorie/. успеxи Мат. Наук, 27, 1972, 231-232. Zbl 0249.57021

[19] Cappell S.E., Shaneson J.L., Some new four-manifolds, Ann. Math., 104, 1976, 61-72. MR 54 #6167 | Zbl 0345.57003

[20] Chern S.S., Hirzebruch F., Serre J.-P., On the index of a fibered manifold, Proc. Amer. Math. Soc., 8, 1957, 587-596. MR 19,441c | Zbl 0083.17801

[21] Conner P.E., Floyd E.E., Torsion in SU-bordism, Memoirs Amer. Math. Soc., 60, 1966. MR 32 #6471 | Zbl 0138.18504

[22] Daccach J.A., The signature and the Kervaire invariant as cobordism invariants, Rutgers Univ. Thesis, 1976.

[23] Guillou L., Marin A., Une extension d'un théorème de Rohlin sur la signature, C.R. Acad. Sci., 285, 18 juillet 1977, 95-98. MR 55 #13440 | Zbl 0361.57018

[24] Hirzebruch F., Topological methods in algebraic geometry, Springer-Verlag, Berlin, Heidelberg, New-York, 1966. MR 34 #2573 | Zbl 0138.42001

[25] Hirzebruch F., Neumann W., Koch S.S., Differentiable manifolds and quadratic forms, Marcel Dekker, New-York, 1971. Zbl 0226.57001

[26] Honda T., Formal groups and zeta-functions, Osaka J. Math., 5, 1968, 199-213. MR 40 #2683 | Zbl 0169.37601

[27] Husemoller D., Fibre bundles, McGraw-Hill, New-York etc, 1966. MR 37 #4821 | Zbl 0144.44804

[28] Jones L.P., The image of the signature homomorphism for symplectic cobordism, Trans. Amer. Math. Soc., 240, 1978, 253-262. MR 58 #13089 | Zbl 0388.57012

[29] Kervaire M.A., Milnor J.W., On 2-spheres in 4-manifolds, Proc. Nat. Acad. Sci. USA, 47, 1961, 1651-1657. MR 24 #A2968 | Zbl 0107.40303

[30] Kervaire M.A., Milnor J.W., Groups of homotopy spheres, I, Ann. Math., 77, 1963, 504-537. MR 26 #5584 | Zbl 0115.40505

[31] Landweber P.S., The signature of symplectic and self-conjugate manifolds, Lecture Notes Math., 741, 1979, 461-472. MR 81c:57037 | Zbl 0419.57008

[32] Milnor J.W., The Steenrod algebra and its dual, Ann. Math., 67, 1958, 150-171. MR 20 #6092 | Zbl 0080.38003

[33] Milnor J.W., Morse theory, Princeton Univ. Press, Princeton, New-Jersey, 1963. MR 29 #634 | Zbl 0108.10401

[34] Milnor J.W., Spin structures on manifolds. Enseignement Math., 9, 1963, 198-203. MR 28 #622 | Zbl 0116.40403

[35] Milnor J.W., On the Stiefel-Whitney numbers of complex manifolds and spin-manifolds, Topology, 3, 1965, 223-230. MR 31 #5207 | Zbl 0132.19601

[36] Milnor J.W., Stasheff J.D., Characteristic classes, Princeton Univ. Press, Princeton, New-Jersey, 1974. MR 55 #13428 | Zbl 0298.57008

[37] Morita S., The Kervaire invariant of hypersurfaces in complex projective spaces, Comment. Math. Helv., 50, 1975, 403-419. MR 52 #6756 | Zbl 0322.57012

[38] Mosher R.E., Tangora M.C., Cohomology operations and applications in homotopy theory, Harper & Row, New-York, Evanston, London, 1968. MR 37 #2223 | Zbl 0153.53302

[39] Надирадӡе Р.Г, (Nadiradze) Инволшии на многобраӡияx Стонга и иx применение в теории кобордиэмов (Involutions sur les variétés de Stong et leurs applications dans la théorie des cobordismes). успеxи мат. наук, 35, 1980, 206-209. Zbl 0445.57021

[40] Novikov S.P., Pontrjagyn classes, the fundamental group and some problems of stable algebra. Essays on topology and related topics, Mém. dédié à G. de Rham, Springer-Verlag, Berlin, Heidelberg, New-York, 1970, 147-155. MR 42 #3804 | Zbl 0199.58401

[41] Ошанин С.Д., Сигнатура SU-многообраӡий. Мат. Ӡаметки, 13, 1973, 97-102.

[41*] Oshanin S.D., The signature of SU-manifolds, Math. notes, 13, 1973, 57-60. MR 49 #3999 | Zbl 0268.57015

[42] Ochanine S., Signature et invariants de Kervaire généralisés, C.R. Acad. Sci., 285, série A, 1977, 211-213. MR 56 #16645 | Zbl 0361.57016

[43] Ochanine S., Formules "à la Hirzebruch" pour les invariants de Kervaire généralisés, C.R. Acad. Sci., 289, série A, 1979, 487-490. MR 80k:55055 | Zbl 0424.57012

[44] Роxлин B.A. / Rokhlin/, Новые реӡультаты в теории четыреxмерныx многообраӡий / Nouveaux résultats dans la théorie des variétés de dimension quatre. Докл. AH CCCP, 84, 1952, 221-224.

[45] Роxлин B.A., Докаӡательство гипотеӡы Гудкова. функц. и прил., 6, 1971, 62-64.

[45*] Rokhlin V.A., Proof of the Gudkov's hypothesis, Func. Anal. and Appl., 6, 1972, 136-138. Zbl 0259.14010

[46] Schwartz J.T., Differential geometry and topology, Notes on Math. and its Appl., New-York, 1968. Zbl 0187.45006

[47] Ш̅Apebи҆ И.P., Ochobatt aattЛ reɃpaИ҆eckoИ ґeometpИИ. «Hayka», Mockba, 1972.

[47*] Shafarevich I.R., Basic algebraic geometry, Springer-Verlag, Berlin, Heidelberg, New-York, 1974. MR 51 #3163 | Zbl 0284.14001

[48] Stong R.E., Notes on cobordism theory, Princeton Univ. Press, Princeton, New-Jersey, 1968. MR 40 #2108 | Zbl 0181.26604

[49] Szczarba R.H., On tangent bundles of fibre spaces and quotient spaces, Amer. J. Math., 86, 1964, 685-697. MR 30 #2522 | Zbl 0151.31703

[50] Wall C.T.C., Addendum to a paper of Conner and Floyd, Proc. Camb. Phil. Soc., 62, 1966, 171-175. MR 32 #6472 | Zbl 0138.18601

[51] Whitehead G.W., Recent advances in homotopy theory, Amer. Math. Soc. Regional conference series in Math., n° 5, 1970. MR 46 #8208 | Zbl 0217.48601

[52] Wood J., Removing handles from non-singular algebraic hypersurfaces in CPn+1, Invent. Math., 31, 1975, 1-3. MR 52 #9253 | Zbl 0313.57022