Volume 22, issue 4 (2018)

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

Volume 26
Issue 8, 3307–3833
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Towers of regular self-covers and linear endomorphisms of tori

Wouter van Limbeek

Geometry & Topology 22 (2018) 2427–2464

Let M be a closed manifold that admits a self-cover p: M M of degree > 1. We say p is strongly regular if all iterates pn: M M are regular covers. In this case, we establish an algebraic structure theorem for the fundamental group of M: We prove that π1(M) surjects onto a nontrivial free abelian group A, and the self-cover is induced by a linear endomorphism of A. Under further hypotheses we show that a finite cover of M admits the structure of a principal torus bundle. We show that this applies when M is Kähler and p is a strongly regular, holomorphic self-cover, and prove that a finite cover of M splits as a product with a torus factor.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

self-cover, holomorphic endomorphism, scale-invariant group, expanding map
Mathematical Subject Classification 2010
Primary: 57N99, 57S17
Secondary: 20F50, 32Q15, 57S15
Received: 12 December 2016
Revised: 22 July 2017
Accepted: 2 September 2017
Published: 5 April 2018
Proposed: Walter Neumann
Seconded: Benson Farb, Leonid Polterovich
Wouter van Limbeek
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States