Pontryagin-Weiss classes and a rational decomposition of spaces of homeomorphisms
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916836292952064 |
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| author | Krannich, Manuel Kupers, Alexander |
| author_facet | Krannich, Manuel Kupers, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20265 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pontryagin-Weiss classes and a rational decomposition of spaces of homeomorphisms Krannich, Manuel Kupers, Alexander Algebraic Topology Geometric Topology 57R20, 57S05, 58D10, 55R40, 18N70 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. |
| title | Pontryagin-Weiss classes and a rational decomposition of spaces of homeomorphisms |
| topic | Algebraic Topology Geometric Topology 57R20, 57S05, 58D10, 55R40, 18N70 |
| url | https://arxiv.org/abs/2504.20265 |