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Group Actions on Aspherical Alexandrov Spaces
Abstract
Conner and Raymond proved that if a connected, compact Lie group G acts effectively on a closed aspherical manifold M, then G is a torus and the fundamental group of G injects into the center of π1(M). We prove the corresponding result for effective isometric actions on closed, aspherical Alexandrov spaces.
Related
- Mapping class group actions on the cohomology of configuration spaces of surfaces
- Group Actions, Fixed Points and Orbit Quotients in Lipschitz Spaces
- On open covers of aspherical spaces satisfying π1-constraints and bounded Adamson cohomology
- Besicovitch Covering on Alexandrov Spaces
- No Connectedness Lemma for Alexandrov spaces
BibTeX
@misc{barcenas2026group,
title = {{Group Actions on Aspherical Alexandrov Spaces}},
author = {Noé Bárcenas and Jesús Núñez-Zimbrón},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32081},
eprint = {2610.32081},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32081},
}
RIS
TY - UNPB
TI - Group Actions on Aspherical Alexandrov Spaces
AU - Noé Bárcenas
AU - Jesús Núñez-Zimbrón
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32081
UR - https://arxiv.org/abs/2610.32081
AB - Conner and Raymond proved that if a connected, compact Lie group G acts effectively on a closed aspherical manifold M, then G is a torus and the fundamental group of G injects into the center of π_1(M). We prove the corresponding result for effective isometric actions on closed, aspherical Alexandrov spaces.
ER -