arXiv Open Access 2024

Homology manifolds and euclidean bundles

Fabian Hebestreit Markus Land Michael Weiss Christoph Winges

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Abstrak

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.

Topik & Kata Kunci

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Penulis (4)

Fabian Hebestreit

Markus Land

Michael Weiss

Christoph Winges

Format Sitasi

APA MLA BibTeX

Hebestreit, F., Land, M., Weiss, M., Winges, C. (2024). Homology manifolds and euclidean bundles. https://arxiv.org/abs/2406.14677

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓