nLab
polyhedron

Contents

This article is about polyhedra in algebraic topology. For polyhedra in convex geometry, see the article polytope.

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

Idea

The study of polyhedra has been one of the sources for methods and applications in algebraic topology, and it is often useful to go back to see the motivations and applications in the older sources. For instance, shape morphisms between polyhedral spaces are just homotopy classes of continuous maps so the Cech invariants of polyhedra coincide with their ordinary ‘standard’ invariants.

Definition

A topological space XX is a polyhedron if it is homeomorphic to the geometric realization of a simplicial complex and hence has a triangulation.

References

(The link gives an up-to-date bibtex reference to the more recent edition of this.)

Last revised on May 2, 2021 at 12:30:23. See the history of this page for a list of all contributions to it.