Crosscap slides and the level 2 mapping class group of a nonorientable surface

Blazej Szepietowski

doi:10.1007/s10711-011-9674-0

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arXiv · 1006.5410

Crosscap slides and the level 2 mapping class group of a nonorientable surface

Blazej Szepietowski

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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.

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BibTeX RIS

Blazej Szepietowski. 2010-06-28. Crosscap slides and the level 2 mapping class group of a nonorientable surface. https://doi.org/10.1007/s10711-011-9674-0

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