A periodicity criterion and the section problem on the Mapping Class Group
Dynamical Systems
2012-02-15 v1 Geometric Topology
Abstract
Some years ago, V. Markovic proved that there is no section of the Mapping Class Group for a closed surface of genus g larger than 5 (in the case of homeomorphims) and more recently generalized this result with D. Saric to the case where g is larger than 1. We will state a periodicity criterion and will use it to simplify some of the arguments given by Markovic and Saric in the proof of their theorem. The periodicity criterion tells us that a homeomorphism of a connected surface must be periodic if the set of connected periodic open sets generates the topology of the surface.
Cite
@article{arxiv.1202.3106,
title = {A periodicity criterion and the section problem on the Mapping Class Group},
author = {Patrice Le Calvez},
journal= {arXiv preprint arXiv:1202.3106},
year = {2012}
}
Comments
40 pages