The bordism version of the h-principle

Details The bordism version of the h-principle The bordism version of the h-principle

2010-02-08

arxiv.org/abs/1002.1650v2

Mathematics

Geometric Topology

30 pages

Scientific paper

In view of the Segal construction each category with operation gives rise to a cohomology theory. We show that similarly each open stable differential relation R determines cohomology theories k^* of solutions and h^* of stable formal solutions of R. We prove that k^* and h^* are equivalent under a mild condition. For example, in the case of the covering differential relation our theorem is equivalent to the Barratt-Priddy-Quillen theorem asserting that the direct limit of classifying spaces B\Sigma_n of permutation groups \Sigma_n of finite sets of n elements is homology equivalent to each path component of the infinite loop space \Omega^{\infty}S^{\infty}.

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