Crosscap slides and the level 2 mapping class group of a nonorientable surface |
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Authors: | B?a?ej Szepietowski |
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Institution: | 1. Institute of Mathematics, Gda??sk University, Wita Stwosza 57, 80-952, Gda??sk, Poland
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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 ${H_1(N;\mathbb{Z}_2)}$ . We also prove that this subgroup is generated by involutions. |
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