Generating the mapping class group of a nonorientable surface by crosscap transpositions
Geometric Topology
2018-03-16 v1
Abstract
A crosscap transposition is an element of the mapping class group of a nonorientable surface represented by a homeomorphism supported on a one-holed Klein bottle and swapping two crosscaps. We prove that the mapping class group of a compact nonorientable surface of genus is generated by conjugates of one crosscap transposition. In the case when the surface is either closed or has one boundary component, we give an explicit set of crosscap transpositions generating the mapping class group.
Cite
@article{arxiv.1703.03611,
title = {Generating the mapping class group of a nonorientable surface by crosscap transpositions},
author = {Marta Leśniak and Błażej Szepietowski},
journal= {arXiv preprint arXiv:1703.03611},
year = {2018}
}