Exotic mapping class group actions on the circle
Geometric Topology
2016-10-18 v3 Group Theory
Abstract
It has been known since the time of Nielsen that the mapping class group of a surface of genus and one puncture acts faithfully by homeomorphisms on the circle. In this note, we show that this standard representation of the mapping class group is not rigid, precisely, if is a finite index subgroup then there exist infinitely many non--conjugate faithful representations . We thus answer a question of B. Farb.
Cite
@article{arxiv.1603.02098,
title = {Exotic mapping class group actions on the circle},
author = {Sang-hyun Kim and Thomas Koberda},
journal= {arXiv preprint arXiv:1603.02098},
year = {2016}
}
Comments
This article has been subsumed by the preprint arXiv:1610.04098. This latter preprint also partially corrects a gap which appeared in this article