Tuesday, January 22, 2019
01/22/2019 - 4:15pm
We will review the technique of building essential immersed closed surfaces out of immersed pants, starting the original applications to surfaces in hyperbolic 3-manifolds and common covers for hyperbolic surfaces. Then we will discuss the applications of these theorems—most notably to the Virtual Haken Theorem—and other settings where surfaces have been constructed or conjectured. These include locally symmetric spaces (both closed and finite volume), the moduli space of Riemann surfaces, and one-ended Gromov hyperbolic spaces.