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

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.

Final version

Cited by in corpus (5)

• On p-almost direct products and residual properties of pure braid groups of nonorientable surfaces
• A minimal generating set of the level 2 mapping class group of a non-orientable surface
• Low dimensional linear representations of the mapping class group of a nonorientable surface
• An infinite presentation for the mapping class group of a non-orientable surface
• Large 1-systems of Curves in Non-orientable Surfaces