Closed Aspherical Manifolds with Center

TL;DR

This paper constructs higher-dimensional closed aspherical manifolds with nontrivial center in their fundamental groups that lack topological circle actions, challenging a previous conjecture.

Contribution

It provides the first examples in dimensions greater than 7 of such manifolds, disproving a conjecture related to Borel's theorem.

Findings

Existence of closed aspherical manifolds with nontrivial center in fundamental groups in all dimensions >7

These manifolds do not admit any topological circle actions

Disproof of the conjectured converse to Borel's theorem

Abstract

We show that in all dimensions >7 there are closed aspherical manifolds whose fundamental groups have nontrivial center but do not possess any topological circle actions. This disproves a conjectured converse (proposed by Conner and Raymond) to a classical theorem of Borel.