The generalized Dehn twist along a figure eight
Geometric Topology
2011-05-05 v2 Algebraic Topology
Group Theory
Abstract
For any unoriented loop on a compact connected oriented surface with one boundary component, the generalized Dehn twist along the loop is defined as an automorphism of the completed group ring of the fundamental group of the surface. If the loop is simple, this is the usual right handed Dehn twist, in particular realized as a mapping class of the surface. We investigate the case when the loop has a single transverse double point, and show that in this case the generalized Dehn twist is not realized as a mapping class.
Keywords
Cite
@article{arxiv.1104.2107,
title = {The generalized Dehn twist along a figure eight},
author = {Yusuke Kuno},
journal= {arXiv preprint arXiv:1104.2107},
year = {2011}
}
Comments
22 pages, 6 figures, 2 tables; minor corrections and modifications have been done in v2