Totally geodesic surfaces in hyperbolic 3-manifolds

Abstract

In this paper we investigate totally geodesic surfaces in hyperbolic 3-maniiblds. In particular we show that if M is a compact arithmetic hyperbolic 3-manifold containing an immersion of a totally geodesic surface then it contains infinitely many commensurability classes of such surfaces. In addition we show for these M that the Chern-Simons invariant is rational. We also show, that unlike the figure-eight knot complement in S3, many knot complements in S3 do not contain an immersion of a closed totally geodesic surface. © 1991, Edinburgh Mathematical Society. All rights reserved.