On Automorphisms of the Hyperelliptic Torelli Group

Geometry Topology Seminar
Monday, February 28, 2011 - 2:05pm for 1 hour (actually 50 minutes)
Skiles 006
Leah Childers – Pittsburg State U
Dan Margalit
We will discuss the structure of the symmetric (or hyperelliptic) Torelli group. More specifically, we will investigatethe group generated by Dehn twists about symmetric separating curvesdenoted by H(S). We will show that Aut(H(S)) is isomorphic to the symmetricmapping class group up to the hyperelliptic involution. We will do this bylooking at the natural action of H(S) on the symmetric separating curvecomplex and by giving an algebraic characterization of Dehn twists aboutsymmetric separating curves.