The Alexander Trick for Homology Spheres

Abstract We show that the group of homeomorphisms of a compact contractible $d$-manifold that fix the boundary is contractible, as long as $d \geq 6$. We deduce this from a strong uniqueness statement for one-sided $h$-cobordisms.

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Publication Details

Journal
Apollo (University of Cambridge)
Published
2024-12-23
DOI
https://doi.org/10.17863/cam.124921
Primary Topic
Geometric and Algebraic Topology
Type
article
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article

The Alexander Trick for Homology Spheres

Søren Galatius, Oscar RANDAL-WILLIAMS
Apollo (University of Cambridge)
Geometric and Algebraic Topology
article

The Alexander Trick for Homology Spheres

Søren Galatius, Oscar RANDAL-WILLIAMS
article en

Abstract

Abstract We show that the group of homeomorphisms of a compact contractible $d$-manifold that fix the boundary is contractible, as long as $d \geq 6$. We deduce this from a strong uniqueness statement for one-sided $h$-cobordisms.

Apollo (University of Cambridge)
Reduced inequalities
Openalex Percentile: Top 37%
Geometric and Algebraic Topology
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The Alexander Trick for Homology Spheres — Søren Galatius, Oscar RANDAL-WILLIAMS · Apollo (University of Cambridge) (2024) | TGRS Research Map | TGRS