Infinitesimal deformations of some SO(3,1) lattices

Published in Pacific Journal of Mathematics, 2000

Recommended citation: Kevin P. Scannell. Infinitesimal deformations of some SO(3, 1) lattices. Pacific Journal of Mathematics, 194(2):455–464, 2000.

DOI: 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.