Volume 18, issue 5 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 5, 2509–3131
Issue 4, 1883–2507
Issue 3, 1259–1881
Issue 2, 635–1258
Issue 1, 1–633

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The action of matrix groups on aspherical manifolds

Shengkui Ye

Algebraic & Geometric Topology 18 (2018) 2875–2895
Abstract

Let SLn() for n 3 be the special linear group and Mr be a closed aspherical manifold. It is proved that when r < n, a group action of SLn() on Mr by homeomorphisms is trivial if and only if the induced group homomorphism SLn() Out(π1(M)) is trivial. For (almost) flat manifolds, we prove a similar result in terms of holonomy groups. In particular, when π1(M) is nilpotent, the group SLn() cannot act nontrivially on M when r < n. This confirms a conjecture related to Zimmer’s program for these manifolds.

Keywords
Nil-manifolds, aspherical manifolds, Zimmer's program, matrix group actions
Mathematical Subject Classification 2010
Primary: 57S25, 57S20
Secondary: 57S17
References
Publication
Received: 20 June 2017
Revised: 19 April 2018
Accepted: 3 June 2018
Published: 22 August 2018
Authors
Shengkui Ye
Department of Mathematical Sciences
Xi’an Jiaotong-Liverpool University
Jiangsu
China
https://yeshengkui.wordpress.com/