Fetching the paper…
Reading the bibliography…
We show that Kervaire invariant one elements in the homotopy groups of spheres exist only in dimensions at most 126.
J. F. Adams, On the non-existence of elements of Hopf invariant one , Ann. of Math. (2) 72
1960
Earlier work this paper cites.
Michel A. Kervaire, A manifold which does not admit any differentiable structure , Comment. Math. Helv. 34
1960
Earlier work this paper cites.
J. W. Milnor, On the cobordism ring Ω ∗ \Omega^{*} and a complex analogue, Part I , American Journal of Mathematics 82
1960
Earlier work this paper cites.
A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. I , Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR MR0132791 (24 #A2627)
1961
Earlier work this paper cites.
Leonard Evens, A generalization of the transfer map in the cohomology of groups , Trans. Amer. Math. Soc. 108
1963
Earlier work this paper cites.
Michel A. Kervaire and John W. Milnor, Groups of homotopy spheres. I , Ann. of Math. (2) 77
1963
Earlier work this paper cites.
J. P. May, The cohomology of restricted Lie algebras and of Hopf algebras , Ph.D. thesis, Princeton University, 1964
1964
Earlier work this paper cites.
J. Lubin and J. Tate, Formal complex multiplication in local fields , Annals of Mathematics 81
1965
Earlier work this paper cites.
M. F. Atiyah, K K -theory and reality , Quart. J. Math. Oxford Ser. (2) 17
1966
Earlier work this paper cites.
Mark Mahowald and Martin Tangora, Some differentials in the Adams spectral sequence , Topology 6
1967
Earlier work this paper cites.
Peter S. Landweber, Conjugations on complex manifolds and equivariant homotopy of M U MU , Bull. Amer. Math. Soc. 74
1968
Earlier work this paper cites.
G. Segal, Classifying spaces and spectral sequences , Inst. Hautes Études Sci. Publ. Math. 34
1968
Earlier work this paper cites.
W. Browder, The Kervaire invariant of framed manifolds and its generalization , Annals of Mathematics 90
1969
Earlier work this paper cites.
M. C. McCord, Classifying spaces and infinite symmetric products , Trans. Amer. Math. Soc. 146
1969
Earlier work this paper cites.
D. G. Quillen, On the formal group laws of unoriented and complex cobordism theory , Bulletin of the American Mathematical Society 75
1969
Earlier work this paper cites.
Peter Gabriel and Friedrich Ulmer, Lokal präsentierbare Kategorien , Lecture Notes in Mathematics, Vol. 221, Springer-Verlag, Berlin, 1971. MR MR0327863 (48 #6205)
1971
Earlier work this paper cites.
A. Grothendieck, Revêtements étales et groupe fondamental (SGA 1) , Documents Mathématiques (Paris) [Mathematical Documents (Paris)], 3, Société Mathématique de France, Paris, 2003, Séminaire de géométrie algébrique du Bois Marie 1960–61. [Algebraic Geometry Seminar of Bois Marie 1960-61], Directed by A. Grothendieck, With two papers by M. Raynaud, Updated and annotated reprint of the 1971 original [Lecture Notes in Math., 224, Springer, Berlin; MR0354651 (50 #7129)]. MR MR2017446 (2004g:14017)
1971
Earlier work this paper cites.
Daniel Quillen, Elementary proofs of some results of cobordism theory using Steenrod operations , Advances in Math. 7
1971
Earlier work this paper cites.
Miguel L. Laplaza, Coherence for distributivity , Coherence in categories, Springer, Berlin, 1972, pp. 29–65. Lecture Notes in Math., Vol. 281. MR 0335598 (49 #379a)
1972
Earlier work this paper cites.
R. James Milgram, Group representations and the Adams spectral sequence , Pacific J. Math. 41
1972
Earlier work this paper cites.
by same author, Homotopical algebra , Lecture Notes in Mathematics, vol. 43, Springer–Verlag, New York, 1972
1972
Earlier work this paper cites.
Andreas W. M. Dress, Contributions to the theory of induced representations , Algebraic K K -theory, II: “Classical” algebraic K K -theory and connections with arithmetic (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Springer, Berlin, 1973, pp. 183–240. Lecture Notes in Math., Vol. 342. MR MR0384917 (52 #5787)
1973
Earlier work this paper cites.
J. F. Adams, Stable homotopy and generalised homology , University of Chicago Press, Chicago, 1974
1974
Earlier work this paper cites.
Klaus Wirthmüller, Equivariant homology and duality , Manuscripta Math. 11
1974
Earlier work this paper cites.
Michikazu Fujii, Cobordism theory with reality , Math. J. Okayama Univ. 18
1975
Earlier work this paper cites.
by same author, Homological properties of comodules over M U ∗ ( M U ) M{\rm U}_{\ast}(M{\rm U}) and BP ∗ (BP) , Amer. J. Math. 98
1976
Earlier work this paper cites.
J. Peter May, E ∞ {E}_{\infty} ring spaces and E ∞ {E}_{\infty} ring spectra , Springer-Verlag, Berlin, 1977, With contributions by Frank Quinn, Nigel Ray, and Jørgen Tornehave, Lecture Notes in Mathematics, Vol. 577. MR 58 #13008
1977
Earlier work this paper cites.
H. R. Miller and D. C. Ravenel, Morava stabilizer algebras and the localization of Novikov’s E 2 E_{2} –term , Duke Mathematical Journal 44
1977
Cited alongside, same era.
H. R. Miller, D. C. Ravenel, and W. S. Wilson, Periodic phenomena in the Adams–Novikov spectral sequence , Annals of Mathematics 106
1977
Cited alongside, same era.
Sören Illman, Smooth equivariant triangulations of G G -manifolds for G G a finite group , Math. Ann. 233
1978
Cited alongside, same era.
John D. S. Jones, The Kervaire invariant of extended power manifolds , Topology 17
1978
Cited alongside, same era.
D. C. Ravenel, The nonexistence of odd primary Arf invariant elements in stable homotopy theory , Math. Proc. Cambridge Phil. Soc. 83
1978
Cited alongside, same era.
A. D. Elmendorf, I. Kriz, M. A. Mandell, and J. P. May, Rings, modules, and algebras in stable homotopy theory , American Mathematical Society, Providence, RI, 1997, With an appendix by M. Cole. MR 97h:55006
1997
Later among the works it cites.
by same author, Localization and completion theorems for M U M{\rm U} -module spectra , Ann. of Math. (2) 146
1997
Later among the works it cites.
Michael J. Hopkins and Jeffrey H. Smith, Nilpotence and stable homotopy theory. II , Ann. of Math. (2) 148
1998
Later among the works it cites.
Saunders MacLane, Categories for the working mathematician , second ed., Graduate Texts in Mathematics, vol. 5, Springer-Verlag, New York, 1998. MR 1712872 (2001j:18001)
1998
Later among the works it cites.
by same author, Notes on the Hopkins-Miller theorem , Homotopy theory via algebraic geometry and group representations (Evanston, IL, 1997), Contemp. Math., vol. 220, Amer. Math. Soc., Providence, RI, 1998, pp. 313–366. MR MR1642902 (2000i:55023)
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Shôrô Araki, Orientations in τ \tau -cohomology theories , Japan. J. Math. (N.S.) 5
1979
Cited alongside, same era.
Tammo tom Dieck, Transformation groups and representation theory , Lecture Notes in Mathematics, vol. 766, Springer, Berlin, 1979. MR 551743 (82c:57025)
1979
Cited alongside, same era.
G. Lewis, J. P. May, and J. McClure, Ordinary R O ( G ) RO(G) -graded cohomology , Bull. Amer. Math. Soc. (N.S.) 4
1981
Cited alongside, same era.
H. R. Miller, On relations between Adams spectral sequences, with an application to the stable homotopy of a Moore space , Journal of Pure and Applied Algebra 20
1981
Cited alongside, same era.
Katsumi Shimomura, Novikov’s Ext 2 {\rm Ext}^{2} at the prime 2 2 , Hiroshima Math. J. 11
1981
Cited alongside, same era.
Gregory Maxwell Kelly, Basic concepts of enriched category theory , London Mathematical Society Lecture Note Series, vol. 64, Cambridge University Press, Cambridge, 1982. MR 651714 (84e:18001)
1982
Cited alongside, same era.
M. G. Barratt, J. D. S. Jones, and M. E. Mahowald, The Kervaire invariant problem , Proceedings of the Northwestern Homotopy Theory Conference (Providence, Rhode Island) (H. R. Miller and S. B. Priddy, eds.), Contemporary Mathematics, vol. 19, American Mathematical Society, 1983, pp. 9–22
1983
Cited alongside, same era.
1998
Later among the works it cites.
by same author, Model categories , Mathematical Surveys and Monographs, vol. 63, American Mathematical Society, Providence, RI, 1999. MR MR1650134 (99h:55031)
1999
Later among the works it cites.
Stefan Schwede and Brooke E. Shipley, Algebras and modules in monoidal model categories , Proc. London Math. Soc. (3) 80
2000
Later among the works it cites.
Po Hu and Igor Kriz, Real-oriented homotopy theory and an analogue of the Adams-Novikov spectral sequence , Topology 40
2001
Later among the works it cites.
M. A. Mandell, J. P. May, S. Schwede, and B. Shipley, Model categories of diagram spectra , Proc. London Math. Soc. (3) 82
2001
Later among the works it cites.
Peter T. Johnstone, Sketches of an elephant: a topos theory compendium. Vol. 1 , Oxford Logic Guides, vol. 43, The Clarendon Press, Oxford University Press, New York, 2002. MR 1953060 (2003k:18005)
2002
Later among the works it cites.
M. A. Mandell and J. P. May, Equivariant orthogonal spectra and S S -modules , Mem. Amer. Math. Soc. 159
2002
Later among the works it cites.
Vladimir Voevodsky, Open problems in the motivic stable homotopy theory. I , Motives, polylogarithms and Hodge theory, Part I (Irvine, CA, 1998), Int. Press Lect. Ser., vol. 3, Int. Press, Somerville, MA, 2002, pp. 3–34. MR MR1977582 (2005e:14030)
2002
Later among the works it cites.
by same author, A possible new approach to the motivic spectral sequence for algebraic K K -theory , Recent progress in homotopy theory (Baltimore, MD, 2000), Contemp. Math., vol. 293, Amer. Math. Soc., Providence, RI, 2002, pp. 371–379. MR MR1890744 (2003g:55011)
2002
Later among the works it cites.
Philip S. Hirschhorn, Model categories and their localizations , Mathematical Surveys and Monographs, vol. 99, American Mathematical Society, Providence, RI, 2003. MR MR1944041 (2003j:18018)
2003
Later among the works it cites.
Stefan Schwede and Brooke Shipley, Equivalences of monoidal model categories , Algebr. Geom. Topol. 3
2003
Later among the works it cites.
Ethan S. Devinatz and Michael J. Hopkins, Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups , Topology 43
2004
Later among the works it cites.
William G. Dwyer, Philip S. Hirschhorn, Daniel M. Kan, and Jeffrey H. Smith, Homotopy limit functors on model categories and homotopical categories , Mathematical Surveys and Monographs, vol. 113, American Mathematical Society, Providence, RI, 2004. MR MR2102294 (2005k:18027)
2004
Later among the works it cites.
Michael A. Mandell, Equivariant symmetric spectra , Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic K K -theory, Contemp. Math., vol. 346, Amer. Math. Soc., Providence, RI, 2004, pp. 399–452. MR 2066508 (2005d:55019)
2004
Later among the works it cites.
by same author, Complex cobordism and stable homotopy groups of spheres , second ed., AMS Chelsea Publishing, vol. 347, American Mathematical Society, 2004
2004
Later among the works it cites.
by same author, On the zero slice of the sphere spectrum , Tr. Mat. Inst. Steklova 246
2004
Later among the works it cites.
Daniel Dugger, An Atiyah-Hirzebruch spectral sequence for K R KR -theory , K K -Theory 35
2006
Later among the works it cites.
J. Adámek, J. Rosický, and E. M. Vitale, What are sifted colimits? , Theory Appl. Categ. 23
2010
Closest in time.
by same author, Algebraic theories , Cambridge Tracts in Mathematics, vol. 184, Cambridge University Press, Cambridge, 2011, A categorical introduction to general algebra, With a foreword by F. W. Lawvere. MR 2757312 (2012f:18001)
2011
Closest in time.
Haynes Miller, Kervaire invariant one [after M. A. Hill, M. J. Hopkins, and D. C. Ravenel] , Astérisque (2012), no. 348, Exp. No. 1029, vii, 65–98, Séminaire Bourbaki: Vol. 2010/2011. Exposés 1027–1042. MR 3050712
2011
Closest in time.
2013
Closest in time.
Anna Marie Bohmann, A comparison of norm maps , Proc. Amer. Math. Soc. 142
2014
Closest in time.