JournalsjemsVol. 18, No. 8pp. 1769–1811

Rational Pontryagin classes and functor calculus

  • Rui Reis

    Universität Münster, Germany
  • Michael S. Weiss

    Universität Münster, Germany
Rational Pontryagin classes and functor calculus cover
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Abstract

It is known that in the integral cohomology of BSO(2m)B \mathrm {SO}(2m), the square of the Euler class is the same as the Pontryagin class in degree 4m4m. Given that the Pontryagin classes extend rationally to the cohomology of BBSTOP(2m2m), it is reasonable to ask whether the same relation between the Euler class and the Pontryagin class in degree 4m4m is still valid in the rational cohomology of BBSTOP(2m2m). In this paper we reformulate the hypothesis as a statement in differential topology, and also in a functor calculus setting.

Cite this article

Rui Reis, Michael S. Weiss, Rational Pontryagin classes and functor calculus. J. Eur. Math. Soc. 18 (2016), no. 8, pp. 1769–1811

DOI 10.4171/JEMS/629