Infinitesimal deformations of some SO(3,1) lattices

Kevin P. Scannell

Vol. 194 (2000), No. 2, 455–464

DOI: 10.2140/pjm.2000.194.455

Abstract

Let Γ be a torsion-free lattice in SO₀(3,1), and let M = Γ∖H³ be the corresponding hyperbolic 3-manifold. It is well-known that in the presence of a closed, embedded, totally-geodesic surface in M, the canonical flat conformal structure on M can be deformed via the bending construction. Equivalently, the lattice Γ admits non-trivial deformations into SO₀(4,1). We present a new construction of infinitesimal deformations for the hyperbolic Fibonacci manifolds, the smallest of which is non-Haken and contains no immersed totally geodesic surface.

Milestones

Received: 21 September 1998

Published: 1 June 2000