Stable Pontryagin-Thom construction for proper maps

2019/05/19 by Csépai, András
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1905.07734

Abstract

We will present proofs for two conjectures stated in arXiv:1808.08073. The first one is that for an arbitrary manifold W, the homotopy classes of proper maps W×ℝⁿ→ℝ^k+n stabilise as n→∞, and the second one is that in a stable range there is a Pontryagin--Thom type bijection for proper maps W×ℝⁿ→ℝ^k+n. The second one actually implies the first one and we shall prove the second one by giving an explicit construction.

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