On quantum moduli space of flat PSL₂(ℝ)-connections on a punctured surface

Abstract

Penner’s decorated Teichmüller space of a punctured surface can be generalized to a decorated moduli space of flat irreducible PSL2(ℝ)-connections with parabolicity conditions around punctures. This space, similarly to the decorated Teichmüller space, admits a parametrization which is well suited for quantization. The quantum ‘ax + b’ group of Woronowicz and Zakrzewski leads to a viable quantum theory.