Abelian subgroups of the homeomorphism group generated by Dehn twists / D. A. Permyakov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2013. № 1. P. 26-32 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].
The subgroup of mapping class group generated by Dehn twists along the set of simple closed pairwise nonhomotopic curves with some conditions is studied. It is proved that this group is isomorphic to a free Abelian group of rank k, where k is the number of curves in the set. In the case of an oriented surface, this result is classic.
Key words: Dehn twist, intersection index of curves, mapping class group.