Closed Aspherical Manifolds with Center
Sylvain Cappell, Shmuel Weinberger, Min Yan

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
