Generating the spin mapping class group by Dehn twists
Annales Henri Lebesgue, Volume 4 (2021), pp. 1619-1658.

KeywordsSpin mapping class group, Dehn twists, curve systems, group generators

### Abstract

Let $\varphi$ be a $ℤ/2ℤ$-spin structure on a closed oriented surface ${\Sigma }_{g}$ of genus $g\ge 4$. We determine a generating set of the stabilizer of $\varphi$ in the mapping class group of ${\Sigma }_{g}$ consisting of Dehn twists about an explicit collection of $2g+1$ curves on ${\Sigma }_{g}$. If $g=3$ then we determine a generating set of the stabilizer of an odd $ℤ/4ℤ$-spin structure consisting of Dehn twists about a collection of $6$ curves.

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