Homology manifolds and euclidean bundles
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929393360699392 |
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| author | Hebestreit, Fabian Land, Markus Weiss, Michael Winges, Christoph |
| author_facet | Hebestreit, Fabian Land, Markus Weiss, Michael Winges, Christoph |
| contents | We construct a Poincaré complex whose periodic total surgery obstruction vanishes but whose Spivak normal fibration does not admit a reduction to a stable euclidean bundle. This contradicts the conjunction of two claims in the literature: Namely, on the one hand that a Poincaré complex with vanishing periodic total surgery obstruction is homotopy equivalent to a homology manifold, which appears in work of Bryant--Ferry--Mio--Weinberger, and on the other that the Spivak normal fibration of a homology manifold always admits a reduction to a stable euclidean bundle, which appears in work of Ferry--Pedersen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14677 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homology manifolds and euclidean bundles Hebestreit, Fabian Land, Markus Weiss, Michael Winges, Christoph Algebraic Topology Geometric Topology We construct a Poincaré complex whose periodic total surgery obstruction vanishes but whose Spivak normal fibration does not admit a reduction to a stable euclidean bundle. This contradicts the conjunction of two claims in the literature: Namely, on the one hand that a Poincaré complex with vanishing periodic total surgery obstruction is homotopy equivalent to a homology manifold, which appears in work of Bryant--Ferry--Mio--Weinberger, and on the other that the Spivak normal fibration of a homology manifold always admits a reduction to a stable euclidean bundle, which appears in work of Ferry--Pedersen. |
| title | Homology manifolds and euclidean bundles |
| topic | Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2406.14677 |