Kervaire invariant one [after M. A. Hill, M. J. Hopkins, and D. C. Ravenel]
Séminaire Bourbaki Volume 2010/2011 Exposés 1027-1042. Avec table par noms d'auteurs de 1948/49 à 2009/10., Astérisque, no. 348 (2012), Talk no. 1029, 34 p.
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Miller, Haynes. Kervaire invariant one [after M. A. Hill, M. J. Hopkins, and D. C. Ravenel], in Séminaire Bourbaki Volume 2010/2011 Exposés 1027-1042. Avec table par noms d'auteurs de 1948/49 à 2009/10., Astérisque, no. 348 (2012), Talk no. 1029, 34 p. http://archive.numdam.org/item/AST_2012__348__65_0/

[1] J. F. Adams - "On the non-existence of elements of Hopf invariant one", Ann. of Math. 72 (1960), p. 20-104. | DOI | MR | Zbl

[2] J. F. Adams, Stable homotopy and generalised homology, University of Chicago Press, 1974. | MR | Zbl

[3] M. G. Barratt, J. D. S. Jones & M. E. Mahowald - "Relations amongst Toda brackets and the Kervaire invariant in dimension 62", J. London Math. Soc. 30 (1984), p. 533-550. | DOI | MR | Zbl

[4] M. G. Barratt, J. D. S. Jones & M. E. Mahowald, "The Kervaire invariant and the Hopf invariant", in Algebraic topology (Seattle, Wash., 1985), Lecture Notes in Math., vol. 1286, Springer, 1987, p. 135- 173. | DOI | MR | Zbl

[5] M. G. Barratt, M. E. Mahowald & M. Tangora - "Some differentials in the Adams spectral sequence. II", Topology 9 (1970), p. 309-316. | DOI | MR | Zbl

[6] W. Browder - "The Kervaire invariant of framed manifolds and its generalization", Ann. of Math. 90 (1969), p. 157-186. | DOI | MR | Zbl

[7] E. H. J. Brown - "Generalizations of the Kervaire invariant", Ann. of Math. 95 (1972), p. 368-383. | DOI | MR | Zbl

[8] J. D. Christensen - "Ideals in triangulated categories: phantoms, ghosts and skeleta", Adv. Math. 136 (1998), p. 284-339. | DOI | MR | Zbl

[9] R. L. Cohen, J. D. S. Jones & M. E. Mahowald - "The Kervaire invariant of immersions", Invent. Math. 79 (1985), p. 95-123. | DOI | EuDML | MR | Zbl

[10] L. Evens - "A generalization of the transfer map in the cohomology of groups", Trans. Amer. Math. Soc. 108 (1963), p. 54-65. | DOI | MR | Zbl

[11] E. D. Farjoun - Cellular spaces, null spaces and homotopy localization, Lecture Notes in Math., vol. 1622, Springer, 1996. | MR | Zbl

[12] P. G. Goerss & M. J. Hopkins - "Moduli spaces of commutative ring spectra", in Structured ring spectra, London Math. Soc. Lecture Note Ser., vol. 315, Cambridge Univ. Press, 2004, p. 151-200. | DOI | MR | Zbl

[13] J. P. C. Greenlees & J. P. May - "Localization and completion theorems for M U -module spectra", Ann. of Math. 146 (1997), p. 509-544. | DOI | MR | Zbl

[14] M. Hazewinkel - Formal groups and applications, Pure and Applied Mathematics, vol. 78, Academic Press Inc., 1978. | MR | Zbl

[15] M. A. Hill, M. J. Hopkins & D. C. Ravenel - "On the nonexistence of elements of Kervaire invariant one", preprint arXiv:0908.3724. | MR | Zbl

[16] P. S. Hirschhorn - Model categories and their localizations, Mathematical Surveys and Monographs, vol. 99, Amer. Math. Soc., 2003. | MR | Zbl

[17] P. Hu & I. Kriz - "Real-oriented homotopy theory and an analogue of the Adams-Novikov spectral sequence", Topology 40 (2001), p. 317-399. | DOI | MR | Zbl

[18] J. D. S. Jones & E. Rees - "Kervaire's invariant for framed manifolds", in Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif, 1976), Part 1, Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., 1978, p. 141-147. | MR | Zbl

[19] M. A. Kervaire - "A manifold which does not admit any differentiable structure", Comment. Math. Helv. 34 (1960), p. 257-270. | DOI | EuDML | MR | Zbl

[20] M. A. Kervaire & J. W. Milnor - "Groups of homotopy spheres. I", Ann. of Math. 77 (1963), p. 504-537. | DOI | MR | Zbl

[21] J. E. Lannes - "Sur l'invariant de Kervaire des variétés fermées stablement parallélisées", Ann. Sci. École Norm. Sup. 14 (1981), p. 183-197. | DOI | EuDML | Numdam | MR | Zbl

[22] G. Lewis, J. P. May & J. Mcclure - "Ordinary RO(G)-graded cohomology", Bull. Amer. Math. Soc. (N.S.) 4 (1981), p. 208-212. | DOI | MR | Zbl

[23] M. E. Mahowald - "Some remarks on the Kervaire invariant problem from the homotopy point of view", in Algebraic topology (Proc. Sympos. Pure Math., Vol XXII, Univ. Wisconsin, Madison, Wis., 1970), Amer. Math. Soc., 1971, p. 165-169. | MR | Zbl

[24] M. E. Mahowald,"A new infinite family in 2 π * s ", Topology 16 (1977), p. 249-256. | DOI | MR | Zbl

[25] M. E. Mahowald & M. Tangora - "On secondary operations which detect homotopy classes", Bol. Soc. Mat. Mexicana 12 (1967), p. 71-75. | MR | Zbl

[26] M. A. Mandell & J. P. May - "Equivariant orthogonal spectra and S -modules", Mem. Amer. Math. Soc. 159 (2002). | MR | Zbl

[27] J. P. May - "The cohomology of restricted Lie algebras and of Hopf algebras : application to the Steenrod algebra", Ph.D. Thesis, Princeton University, 1964. | MR

[28] H. R. Miller - "On relations between Adams spectral sequences, with an application to the stable homotopy of a Moore space", J. Pure Appl. Algebra 20 (1981), p. 287-312. | DOI | MR | Zbl

[29] H. R. Miller, D. C. Ravenel & W. S. Wilson - "Periodic phenomena in the Adams-Novikov spectral sequence", Ann. of Math. 106 (1977), p. 469-516. | DOI | MR | Zbl

[30] S. P. Novikov - "Methods of algebraic topology from the point of view of cobordism theory", Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), p. 855-951. | MR | Zbl

[31] D. G. Quillen - Homotopical algebra, Lecture Notes in Math., No. 43, Springer, 1967. | MR | Zbl

[32] D. G. Quillen,"Elementary proofs of some results of cobordism theory using Steenrod operations", Advances in Math. 7 (1971), p. 29-56. | DOI | MR | Zbl

[33] D. C. Ravenel - "The non-existence of odd primary Arf invariant elements in stable homotopy", Math. Proc. Cambridge Philos. Soc. 83 (1978), p. 429-443. | DOI | MR | Zbl

[34] D. C. Ravenel, Complex cobordism and stable homotopy groups of spheres, vol. 347, AMS Chelsea Publishing, 2004. | Zbl

[35] C. Rezk - "Notes on the Hopkins-Miller theorem", in Homotopy theory via algebraic geometry and group representations (Evanston, IL, 1997), Contemp. Math., vol. 220, Amer. Math. Soc., 1998, p. 313-366. | DOI | MR | Zbl

[36] J. S. P. Wang - "On the cohomology of the mod - 2 Steenrod algebra and the non-existence of elements of Hopf invariant one", Illinois J. Math. 11 (1967), p. 480-490. | MR | Zbl