A combinatorial algorithm to compute presentations of mapping class groups of orientable surfaces with one boundary component

Abstract

Abstract We give an algorithm which computes a presentation for a subgroup, denoted 𝒜ℳ g,p,1 ${\mathcal {AM}_{g,p,1}}$ , of the automorphism group of a free group. It is known that 𝒜ℳ g,p,1 ${\mathcal {AM}_{g,p,1}}$ is isomorphic to the mapping class group of an orientable genus-g surface with p punctures and one boundary component. We define a variation of the Auter space.