# Teichmüller space and the 9g-9 theorem

## Location

384I

Friday, February 11, 2022 4:00 PM

Nikhil Pandit (Stanford)

After introducing and topologizing Teichmüller space, we will use Fenchel-Nielsen coordinates to sketch a proof that the Teichmüller space of a closed surface S_g, g≥2, is homeomorphic to a (6g-6)-dimensional ball. Next we’ll discuss the 9g-9 theorem, which says that elements of Teich(S_g) are determined by the lengths they assign to 9g-9 fixed simple closed curves on the surface.