R. C. Penner
Published 2004-10-28, updated 2006-05-02Version 2
A classical combinatorial fact is that the simplicial complex consisting of disjointly embedded chords in a convex planar polygon is a sphere. For any surface F with non-empty boundary, there is an analogous complex Arc(F) consisting of suitable equivalence classes of arcs in F connecting its boundary components. The main result of this paper is the determination of those arc complexes Arc(F) that are also spherical. This classification has consequences for Riemann's moduli space via its known identification with an analogous arc complex in the punctured case with no boundary. Namely, the essential singulities of the natural cellular compactification can be described.
Comments: 33 pages, 17 figures; corrected Lemma 9, and retracted stratified structure theorem
Cell decomposition and compactification of Riemann's moduli space in decorated Teichmüller theory
Erratum to "Cobordisms of maps with singularities of given class"
Flexibility of singularities and beyond
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