On the orbifold fundamental group of the odd component of the stratum H(2,...,2)

Ursula Hamenstädt

Published 2020-02-19Version 1

Let Sg be a closed oriented surface of genus g>2 and let G be the orbifold fundamental group of the odd component of the stratum PH(2,...,2) of projective abelian differentials on Sg. We show that G is a quotient of an explicit small type Artin group with 3g-2 generators. We also determine for all g>2 a generating set of the stabilizer of an odd spin structure in the mapping class group of Sg consisting of Dehn twists about an explicit collection of 2g+1 curves in Sg.