English

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 g7g\ge 7 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 g+2g+2 crosscap transpositions generating the mapping class group.

Keywords

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}
}
R2 v1 2026-06-22T18:42:08.355Z