Metric topology on the moduli space

Abstract

We define the smooth Lipschitz topology on the moduli space and show that each conformal class is dense in the moduli space endowed with Gromov-Hausdorff topology, which offers an answer to Tuschmann’s question.

Keywords

• gromov-hausdorff topology
• ε-topology
• lipschitz-topology
• smooth lipschitz-topology