[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 52 (1002ﾚｽ)

Inter-universal geometry と ABC予想 (応援スレ) 52 http://rio2016.5ch.net/test/read.cgi/math/1613784152/

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533: １３２人目の素数さん [] 2021/03/02(火) 13:18:56.05 ID:brRFu6nO >>532 ＜メモ＞ 余談ですが 下記のBernoulli number ”6.5 Use in topology” によれば、「ES_n ＝ 2^{2n-2} - 2^{4n-3}) Numerator (B_{4n}/{4n}).」という式があるらしいね （参考） https://en.wikipedia.org/wiki/Bernoulli_number#Use_in_topology Bernoulli number Contents 6 Applications of the Bernoulli numbers 6.5 Use in topology Use in topology The Kervaire–Milnor's formula for the order of the cyclic group of diffeomorphism classes of exotic (4n − 1)-spheres which bound parallelizable manifolds involves Bernoulli numbers. Let ESn be the number of such exotic spheres for n ＞＝ 2, then ES_n ＝ 2^{2n-2} - 2^{4n-3}) Numerator (B_{4n}/{4n}). The Hirzebruch signature theorem for the L genus of a smooth oriented closed manifold of dimension 4n also involves Bernoulli numbers. http://rio2016.5ch.net/test/read.cgi/math/1613784152/533

537: Schlecht [sage] 2021/03/02(火) 17:51:22.87 ID:ozN2NqQb >>533 異種球面より球面の安定ホモトピー群の方が本質的だよ https://en.wikipedia.org/wiki/Homotopy_groups_of_spheres https://en.wikipedia.org/wiki/J-homomorphism Image of the J-homomorphism If r=4n-1 is 3 mod 4 and positive the image is a cyclic group of order equal to the denominator of B_{2n}/4n, where B_{2n}} is a Bernoulli number. http://rio2016.5ch.net/test/read.cgi/math/1613784152/537

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