Homology manifolds and euclidean bundles
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 vanishin...
Saved in:
Published in | arXiv.org |
---|---|
Main Authors | , , , |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
20.06.2024
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | 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. |
---|---|
ISSN: | 2331-8422 |