Planes in degenerate 3-manifolds

2016/04/07 by Mj, Mahan
#30F40 #37A17 #37B20 #57M50 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1604.01976

Abstract

We study totally geodesic planes in hyperbolic 3-manifolds M having incompressible core and degenerate ends. We prove a Ratner-type phenomenon: a closed minimal PSL(2,R)-invariant subset of M is either an immersed totally geodesic surface or all of M. We also show that for an arbitrary infinite volume hyperbolic 3-manifold M without parabolics and with finitely generated fundamental group, the number of compact totally geodesic surfaces in M is finite.

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