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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/