Probing mapping class groups using arcs
Robert Clark Penner · Proceedings of symposia in pure mathematics · 2006
The action of the mapping class group of a surface on the collection of homotopy classes of disjointly embedded curves or arcs in the surface is discussed here as a tool for understanding Riemann's moduli space and its topological and geometric invariants.Furthermore, appropriate completions, elaborations, or quotients of the set of all such homotopy classes of curves or arcs give Thurston's boundary for Teichmüller space or a combinatorial description of moduli space in terms of fatgraphs.Related open problems and questions are discussed.