Iterated finite group actions on closed connected aspherical manifolds

TL;DR

This paper investigates the properties of iterated finite group actions on aspherical manifolds, introducing new concepts like the length of an iterated action and deriving rigidity results for various classes of manifolds.

Contribution

It introduces the concept of the length of an iterated action and applies it to study rigidity and symmetry properties of aspherical manifolds.

Findings

Rigidity results for aspherical manifolds under iterated actions

Definition and analysis of the length of an iterated action

Application to nilmanifolds, solvmanifolds, and locally symmetric spaces

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.