Generating the mapping class group of a nonorientable surface by crosscap transpositions

Marta Leśniak; Błażej Szepietowski

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arXiv · 1703.03611

Generating the mapping class group of a nonorientable surface by crosscap transpositions

Marta Leśniak·Błażej Szepietowski

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Abstract

A crosscap transposition is an element of the mapping class group of a nonorientable surface represented by a homeomorphism supported on a one-holed Klein bottle and swapping two crosscaps. We prove that the mapping class group of a compact nonorientable surface of genus $g\ge 7$ is generated by conjugates of one crosscap transposition. In the case when the surface is either closed or has one boundary component, we give an explicit set of $g+2$ crosscap transpositions generating the mapping class group.

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Marta Leśniak, Błażej Szepietowski. 2017-03-10. Generating the mapping class group of a nonorientable surface by crosscap transpositions. https://arxiv.org/abs/1703.03611

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