English

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.

Keywords

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

R2 v1 2026-06-21T15:41:59.040Z