Geometry & Topology
- Geom. Topol.
- Volume 15, Number 3 (2011), 1545-1567.
Free planar actions of the Klein bottle group
We describe the structure of the free actions of the fundamental group of the Klein bottle by orientation preserving homeomorphisms of the plane. The main result is that must act properly discontinuously, while 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.
Geom. Topol., Volume 15, Number 3 (2011), 1545-1567.
Received: 25 January 2011
Revised: 25 January 2011
Accepted: 29 June 2011
First available in Project Euclid: 20 December 2017
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Le Roux, Frédéric. Free planar actions of the Klein bottle group. Geom. Topol. 15 (2011), no. 3, 1545--1567. doi:10.2140/gt.2011.15.1545. https://projecteuclid.org/euclid.gt/1513732339