Geometric subgroups of mapping class groups

  title={Geometric subgroups of mapping class groups},
  author={Luis Paris Dale Rolfsen}
This paper is a study of the subgroups of mapping class groups of Riemann surfaces, called “geometric” subgroups, corresponding to the inclusion of subsurfaces. Our analysis includes surfaces with boundary and with punctures. The centres of all the mapping class groups are calculated. We determine the kernel of inclusion-induced maps of the mapping class group of a subsurface, and give necessary and sufficient conditions for injectivity. In the injective case, we show that the commensurability… CONTINUE READING