Totally geodesic submanifolds of Teichmuller space

2017/02/10 by Wright, Alex
#Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1702.03249

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.

Related

• The geometry of totally geodesic subvarieties of moduli spaces of Riemann surfaces
• Totally geodesic subvarieties of the moduli space of curves and linear systems
• The boundary of a totally geodesic subvariety of moduli space
• Hopf fibrations and totally geodesic submanifolds
• Isometric embeddings of Teichmüller spaces are covering constructions