nLab
Conner-Floyd isomorphism

Contents

Idea

Conner-Floyd isomorphism is an isomorphism

K *(X)U *(X) Ω U K^*(X)\cong U^*(X)\otimes_{\Omega_U}\mathbb{Z}

where Ω U\Omega_U is the cobordism ring of almost complex manifolds and \mathbb{Z} has a structure of Ω U\Omega_U-module via the Todd class.

Literature and variants

  • P. E. Conner, E. E. Floyd, The relation of cobordism to KK-theories, Lecture Notes in Mathematics 28 Springer 1966 v+112 pp. MR216511

Russian transl. of above: Коннер П., Флойд Э. 0 соотношении теории кобордизмов и К-теории. - Дополнение к кн.: Гладкие периодические отображения. - М.: Мир, 1969. djvu

  • Gerhard Wolff, Der Einfluss von K *()K^{\ast} (-) auf U *()U^{\ast} (-), Manuscripta Math. 10 (1973), 141–-161

  • Gerhard Wolff, Vom Conner-Floyd Theorem zum Hattori-Stong Theorem, Manuscripta Math. 17 (1975), no. 4, 327–-332, doi, MR388420

For an equivariant generalization see

  • Steven R. Costenoble, Equivariant Conner-Floyd isomorphism, Trans. Amer. Math. Soc. 304, No. 2 (Dec., 1987), 801–818, jstor

There is also a motivic version. See

  • David Gepner, Victor Snaith, On the motivic spectra representing algebraic cobordism and algebraic K-theory, Doc. Math., 14:359–396 (electronic), 2009, pdf

Last revised on February 16, 2016 at 14:49:39. See the history of this page for a list of all contributions to it.