The twist subgroup of the mapping class group of a nonorientable surface

Abstract

Let T(N) be the subgroup of the mapping class group of a nonorientable surface N (possibly with punctures and/or boundary components) generated by twists about two-sided circles. We obtain a simple generating set for T(N). As an application we compute the first homology group (abelianization) of T(N).

References in corpus (3)

• A presentation for the mapping class group of the closed non-orientable surface of genus 4
• Generating mapping class groups of nonorientable surfaces with boundary
• A presentation for the mapping class group of a non-orientable surface from the action on the complex of curves

Cited by in corpus (1)

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