Crosscap slides and the level 2 mapping class group of a nonorientable surface
Geometric Topology
2017-02-09 v3
Abstract
Crosscap slide is a homeomorphism of a nonorientable surface of genus at least 2, which was introduced under the name Y-homeomorphism by Lickorish as an example of an element of the mapping class group which cannot be expressed as a product of Dehn twists. We prove that the subgroup of the mapping class group of a closed nonorientable surface N generated by all crosscap slides is equal to the level 2 subgroup consisting of those mapping classes which act trivially on H_1(N;Z_2). We also prove that this subgroup is generated by involutions.
Cite
@article{arxiv.1006.5410,
title = {Crosscap slides and the level 2 mapping class group of a nonorientable surface},
author = {Blazej Szepietowski},
journal= {arXiv preprint arXiv:1006.5410},
year = {2017}
}
Comments
Final version