Rational Pontryagin classes and functor calculus
Algebraic Topology
2015-03-03 v5
Abstract
It is known that in the integral cohomology of BSO(2m), the square of the Euler class is the same as the Pontryagin class in degree 4m. Given that the Pontryagin classes extend rationally to the cohomology of BSTOP(2m), it is reasonable to ask whether the same relation between the Euler class and the Pontryagin class in degree 4m is still valid in the rational cohomology of BSTOP(2m). In this paper we use smoothing theory and tools from homotopy theory to reformulate the hypothesis, and variants, in a differential topology setting and in a functor calculus setting.
Cite
@article{arxiv.1102.0233,
title = {Rational Pontryagin classes and functor calculus},
author = {Rui M. G. Reis and Michael S. Weiss},
journal= {arXiv preprint arXiv:1102.0233},
year = {2015}
}
Comments
Very minor changes in the last revision