Totally geodesic submanifolds of Teichmuller space

Abstract

We show that any totally geodesic submanifold of Teichmuller space of dimension greater than one covers a totally geodesic subvariety, and only finitely many totally geodesic subvarieties of dimension greater than one exist in each moduli space.Comment: This is a post-publication version which corrects an error pointed out by Frederik Benirschke. No change is required to any of the main results. An erratum describing the changes is also available at https://websites.umich.edu/~alexmw/TotGeodesicErratum.pdf and will appear in the journa