Generating the spin mapping class group by Dehn twists

Hamenstädt, Ursula

doi:10.5802/ahl.112

Hamenstädt, Ursula

Generating the spin mapping class group by Dehn twists

Annales Henri Lebesgue, Volume 4 (2021), pp. 1619-1658.

Metadata

DOI10.5802/ahl.112

Keywords Spin mapping class group, Dehn twists, curve systems, group generators

Abstract

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

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