Probing mapping class groups using arcs
Geometric Topology
2007-05-23 v2 Algebraic Topology
Abstract
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 for instance Thurston's boundary for Teichm\"uller space or a combinatorial description of moduli space in terms of fatgraphs. Related open problems and questions are discussed.
Cite
@article{arxiv.math/0505595,
title = {Probing mapping class groups using arcs},
author = {R. C. Penner},
journal= {arXiv preprint arXiv:math/0505595},
year = {2007}
}
Comments
21 pages, 6 figures, expanded version