nLab Alexander's trick

Contents

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Contents

Statement

Consider the mapping space of those homeomorphisms from the closed ball D n+1D^{n+1} to itself which restrict to the identity on the boundary n n -sphere. What is known as Alexander’s trick is a construction (due to Alexander 1923) of an explicit deformation which witnesses that this space is connected, hence that any two such homemorphisms are connected by an isotopy.

References

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Created on September 20, 2022 at 12:38:36. See the history of this page for a list of all contributions to it.