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

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

2010-06-28

arxiv.org/abs/1006.5410v2

Mathematics

Geometric Topology

A few mistakes corrected, some clarifications and one reference added. Now 19 pages, 9 figures

Scientific paper

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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