Iterated finite group actions on closed connected aspherical manifolds

2025/06/16 by Serrano, Jordi Daura
#54H15 #57S17 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.13184

Abstract

In this paper we use free iterated actions and the iterated discrete degree of symmetry to obtain rigidity results on aspherical manifolds. We also introduce the concept of the length of an iterated action and we study it for nilmanifolds, solvmanifolds and locally symmetric spaces.

Citations

• Large and iterated finite group actions on manifolds admitting non-zero degree maps to nilmanifolds
• Actions of large finite groups on aspherical manifolds
• Actions of large finite groups on manifolds
• Finite groups acting on compact complex parallelizable manifolds
• Discrete degree of symmetry of manifolds
• Iterated circle bundles and infranilmanifolds
• The Jordan property for Lie groups and automorphism groups of complex\n spaces
• Structure of normally and finitely non-co-Hopfian groups
• A Users' Guide to Infra-nilmanifolds and Almost-Bieberbach groups
• Half-BPS M2-brane orbifolds
• The Borel Conjecture for hyperbolic and CAT(0)-groups
• Do manifolds have little symmetry?

Related

• Actions of large finite groups on aspherical manifolds
• Large and iterated finite group actions on manifolds admitting non-zero degree maps to nilmanifolds
• Symmetries of exotic aspherical space forms
• Gluing locally symmetric manifolds: asphericity and rigidity
• Almost-quasifibrations and fundamental groups of orbit configuration spaces