Moduli of contact circles

Abstract

We continue the study of linear families of contact forms on 3-manifolds begun in our paper `Contact geometry and complex surfaces'. The present paper introduces Teichmuller and moduli spaces for so-called taut contact circles. By constructing a developing map for taut contact circles, we show that these geometrically defined deformation spaces are equivalent to certain spaces of representations of the fundamental group in appropriate Lie groups. Furthermore, we relate these deformation spaces to `classical' Teichmuller theory of Riemann surfaces and orbifolds.

49 pages, 2 figures