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arXiv · 2504.20265

Pontryagin-Weiss classes and a rational decomposition of spaces of homeomorphisms

Manuel Krannich·Alexander Kupers
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Abstract

We construct a rational homotopy pullback decomposition for variants of the classifying space of the group of homeomorphisms for a large class of manifolds. This has various applications, including a rational section of the stabilisation map ${\rm Top}(d)\rightarrow {\rm Top}$ of the space of homeomorphisms of ${\bf R}^d$ for $d\ge 6$, or a new method to construct topological bundles and detect characteristic classes thereof. Some steps in the proofs may be of independent interest, such as the construction of a nullhomotopy of the twice-iterated stabilisation map for the space of orientation-preserving derived automorphisms of the rational $E_d$-operad, results on recovering boundaries of manifolds from the interior in the context of embedding calculus, or a treatment of tensor products of truncated $\infty$-operads.

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BibTeXRIS

Manuel Krannich, Alexander Kupers. 2025-04-28. Pontryagin-Weiss classes and a rational decomposition of spaces of homeomorphisms. https://arxiv.org/abs/2504.20265

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