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 A001676 Number of h-cobordism classes of smooth homotopy n-spheres. (Formerly M5197 N2261) 14
 1, 1, 1, 1, 1, 1, 28, 2, 8, 6, 992, 1, 3, 2, 16256, 2, 16, 16, 523264, 24, 8, 4, 69524373504, 2, 4, 12, 67100672, 2, 3, 3, 7767211311104, 8, 32, 32, 3014494287036416, 6, 24, 120, 2303837503821447168, 192, 32, 96, 341653284209033216, 8, 11520, 48, 798366828940770681028608, 32, 12, 24, 11852230872517975212032, 24, 32, 8, 91678339751618435453288448, 2, 16, 4, 1986677733776616536315084668928, 4, 1, 24, 142211872163171481167115958878208 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS For n not equal to 4 (and possibly for all n) this is the number of oriented diffeomorphism classes of differentiable structures on the n-sphere. a(3) = 1 follows now that the PoincarĂ© conjecture has been proved. a(n) for n != 4 is the order of S_n, the n-th group in Tables 1 and 2 (explained in Further Details p. 807) of Milnor 2011. REFERENCES S. S. Khare, On Abel Prize 2011 to John Willard Milnor, Math. Student, 82 (2013), 247-279. S. O. Kochman, Stable homotopy groups of spheres. A computer-assisted approach. Lecture Notes in Mathematics, 1423. Springer-Verlag, Berlin, 1990. 330 pp. ISBN: 3-540-52468-1. [Math. Rev. 91j:55016] S. O. Kochman and M. E. Mahowald, On the computation of stable stems. The Cech Centennial (Boston, MA, 1993), 299-316, Contemp. Math., 181, Amer. Math. Soc., Providence, RI, 1995. [Math. Rev. 96j:55018] J. P. Levine, Lectures on groups of homotopy spheres. In Algebraic and geometric topology (New Brunswick, NJ, 1983), 62-95, Lecture Notes in Math., 1126, Springer, Berlin, 1985. J. W. Milnor and J. D. Stasheff, Characteristic Classes, Princeton, 1974, p. 285. S. P. Novikov ed., Topology I, Encyc. of Math. Sci., vol. 12. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). H. Whitney, The work of John W. Milnor, pp. 48-50 of Proc. Internat. Congress Mathematicians, Stockholm, 1962. LINKS T. Copeland, The Kervaire-Milnor formula A. Hatcher, Stable Homotopy Groups of Spheres M. A. Kervaire and J. W. Milnor, Groups of homotopy spheres: I, Ann. of Math. (2) 77 1963 504-537. Alexander Kupers, Lectures on diffeomorphism groups of manifolds, Version April 28, 2018. J. W. Milnor, On manifolds homeomorphic to the 7-sphere, Ann. of Math. 64 (1956), 399-405. John W. Milnor, Differential Topology Forty-six Years Later, Notices Amer. Math. Soc. 58 (2011), 804-809. John W. Milnor, Spheres, Abel Prize lecture (video), 2011. G. D. Rizell, J. D. Evans, Exotic spheres and the topology of symplectomorphism groups, J. Topol. 8 (2015) 586-602 N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98). Eric Weisstein's World of Mathematics, Exotic Sphere. Wikipedia, Exotic sphere CROSSREFS Cf. A047680, A053381, A057617, A048648, A187595, A187717, A189995, A228689, A228690, A228691, A228692. Sequence in context: A257835 A040780 A040781 * A040782 A040783 A057617 Adjacent sequences:  A001673 A001674 A001675 * A001677 A001678 A001679 KEYWORD nonn,hard,nice,changed AUTHOR EXTENSIONS More terms from Paul Muljadi, Mar 17 2011 Further terms from Jonathan Sondow, Jun 16 2011 STATUS approved

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Last modified December 1 06:09 EST 2020. Contains 338833 sequences. (Running on oeis4.)