Circular groups, planar groups, and the Euler class
| dc.creator | Calegari, Danny | |
| dc.date | 2004-03-18 | |
| dc.date | 2004-12-24 | |
| dc.date.accessioned | 2026-07-07T05:06:32Z | |
| dc.date.available | 2026-07-07T05:06:32Z | |
| dc.description | We study groups of C^1 orientation-preserving homeomorphisms of the plane, and pursue analogies between such groups and circularly-orderable groups. We show that every such group with a bounded orbit is circularly-orderable, and show that certain generalized braid groups are circularly-orderable. We also show that the Euler class of C^infty diffeomorphisms of the plane is an unbounded class, and that any closed surface group of genus >1 admits a C^infty action with arbitrary Euler class. On the other hand, we show that Z oplus Z actions satisfy a homological rigidity property: every orientation-preserving C^1 action of Z oplus Z on the plane has trivial Euler class. This gives the complete homological classification of surface group actions on R^2 in every degree of smoothness. | |
| dc.description | Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon7/paper15.abs.html | |
| dc.identifier | https://arxiv.org/abs/math/0403311 | |
| dc.identifier | http://arxiv.org/abs/math/0403311 | |
| dc.identifier | Geom. Topol. Monogr. 7 (2004) 431-491 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70507 | |
| dc.subject | Geometric Topology | |
| dc.subject | Dynamical Systems | |
| dc.subject | Group Theory | |
| dc.subject | 37C85, 37E30, 57M60 | |
| dc.title | Circular groups, planar groups, and the Euler class | |
| dc.type | text |