Geometry of geodesic currents

Geometry & Topology
Event time: 
Tuesday, December 6, 2022 - 3:00pm
LOM 202
Jenya Sapir
Speaker affiliation: 
Binghamton University
Event description: 

The space of projective, filling currents PFC(S) contains many structures relating to a closed, genus g surface S. For example, it contains the set of all closed curves on S, as well as an embedded copy of Teichmuller space, and many other spaces of metrics on S. We show that the symmetrized Thurston metric on Teichmuller space naturally extends to a complete, proper metric on PFC(S). We will then discuss the geometry of PFC(S) under this metric.