Volume 15, issue 3 (2011)

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

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

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
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Free planar actions of the Klein bottle group

Frédéric Le Roux

Geometry & Topology 15 (2011) 1545–1567
Abstract

We describe the structure of the free actions of the fundamental group of the Klein bottle a,baba1 = b1 by orientation preserving homeomorphisms of the plane. The main result is that a must act properly discontinuously, while b cannot act properly discontinuously. As a corollary, we describe some torsion free groups that may not act freely on the plane. We also find some properties which are reminiscent of Brouwer theory for the group , in particular that every free action is virtually wandering.

Keywords
plane homeomorphism, free group action
Mathematical Subject Classification 2000
Primary: 37E30, 57S25
References
Publication
Received: 25 January 2011
Revised: 25 January 2011
Accepted: 29 June 2011
Published: 5 September 2011
Proposed: Danny Calegari
Seconded: Leonid Polterovich, Walter Neumann
Authors
Frédéric Le Roux
Laboratoire de Mathématiques, CNRS UMR 8628
Université Paris Sud 11
F-91405 Orsay Cedex
France
http://www.math.u-psud.fr/~leroux/