Regenerating singular hyperbolic structures from Sol
by
Michael Heusener
Université Blaise Pascal, Aubière, France

Let M be a torus bundle over S¹ with an orientation preserving Anosov monodromy. The manifold M admits a geometric structure modeled on Sol. We prove that the Sol structure can be deformed into singular hyperbolic cone structures whose singular locus \Sigma subset M is the mapping torus of the fixed point of the monodromy.

The hyperbolic cone metrics are parametred by the cone angle \alpha in the interval (0, 2\pi). When \alpha --> 2\pi, the cone manifolds collapse to the basis of the fibration S¹, and they can be rescaled in the direction of the fibers to converge to the Sol manifold.

Date received: February 28, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafv-57.