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Homogeneous locally compact spaces

Vesko Valov

Abstract

This is a survey of the recent results and unsolved problems about locally compact homogeneous metric spaces. Mostly, homogeneous finite-dimensional $ANR$-spaces are discussed.

Homogeneous locally compact spaces

Abstract

This is a survey of the recent results and unsolved problems about locally compact homogeneous metric spaces. Mostly, homogeneous finite-dimensional -spaces are discussed.
Paper Structure (4 sections, 13 theorems, 1 equation)

This paper contains 4 sections, 13 theorems, 1 equation.

Table of Contents

  1. Introduction
  2. Homogeneous spaces and the Bing-Borsuk conjecture
  3. Homogeneous $ANR$-spaces
  4. Separation of homogeneous spaces

Key Result

Theorem 2.4

bre,br2 If $X$ is a locally compact homogeneous $ANR$-space of dimension $n$ such that the groups $H_k(X,X\setminus\{x\};\mathbb Z)$, $k\leq n$, are finitely generated, then $X$ is a generalized $n$-manifold.

Theorems & Definitions (14)

  • Conjecture 2.3
  • Theorem 2.4
  • Theorem 2.5
  • Theorem 2.6
  • Theorem 2.7
  • Theorem 3.1
  • Theorem 3.2
  • Corollary 3.3
  • Theorem 3.5
  • Theorem 3.6
  • ...and 4 more