The topology of finite group actions on Riemann surfaces and of their moduli spaces.

Time: 9:30 - 11h00, 19th June

Venue: Room 507, A6, Institute of Mathematics

Abstract: Let G be a finite group. We consider effective G-actions on a compact, connected, oriented topological surface S of genus g. We review the classification of such actions, following Nielsen (in the case where G is cyclic), Edmonds (for G abelian), Livingston-Zimmermann-Dunfield-Thurston (for free actions) and Catanese-Loenne-P. On the other hand, endowing S with the structure of Riemann surface, one can consider moduli spaces of such G-actions (that have been studied also in connection with the Inverse Galois Problem (e. g. by Fried-Voelklein) and with the Cohen-Lenstra conjecture (e.g. by Ellenberg-Venkatesh-Westerland)). In the seminar we will briefly present some of the topological properties of these moduli spaces that follow from the above classification.