Mapping class group

Given a Riemann surface $ F_{g,n}$ of genus $ g$ with $ n$ boundary components, the mapping class group $ \Gamma_{g,n}$ is the group of diffeomorphisms of $ F_{g,n}$ which fix the boundary pointwise, modulo the subgroup of diffeomorphisms isotopic to the identity. Equivalently, it is the group of connected components $ \pi_0

Jeffrey Herschel Giansiracusa 2005-06-27