Characterizations of $G$-ANR spaces and inverse limits

Sergey A. Antonyan; Aura Lucina Kantún-Montiel; Jesús Eduardo Mata-Cano; Armando Mata-Romero

doi:10.48550/arxiv.2601.07027

Characterizations of $G$-ANR spaces and inverse limits

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Sergey A. Antonyan, Aura Lucina Kantún-Montiel, Jesús Eduardo Mata-Cano, Armando Mata-Romero

DOI: 10.48550/arxiv.2601.07027

Cited by: 0

Abstract

In this paper we prove that, for a compact group $G$, a metrizable $G$-space is a $G$-ANR under the following asumptions: (1) if it dominates a $G$-ANR space through a fine $G$-homotopy equivalence; (2) if it is $G$-homotopy dense in a $G$-ANR; (3) if it contains a $G$-ANR as a $G$-homotopy dense subset; (4) if it is the inverse limit of an inverse sequence of $G$-ANR spaces with bonding maps that are fine $G$-homotopy equivalences.

Fields of Study & Subjects

Geometric and Algebraic Topology Advanced Topology and Set Theory Homotopy and Cohomology in Algebraic Topology

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 11 January 2026
Document type: Preprint