We consider Riemann surfaces of infinite type and their reduced Teichmüller spaces. The reduced Teichmüller space admits the action of the reduced mapping class group. Generally, the action is not discrete while it is faithful. We give sufficient conditions for the discreteness of the action in terms of the geometry of Riemann surfaces.
Ege FUJIKAWA. Hiroshige SHIGA. Masahiko TANIGUCHI. "On the action of the mapping class group for Riemann surfaces of infinite type." J. Math. Soc. Japan 56 (4) 1069 - 1086, October, 2004. https://doi.org/10.2969/jmsj/1190905449