14 citations · 32 across the 7 of their papers we have counts for
6 papers · 1 filter
Probing mapping class groups using arcs
R. C. Penner
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 unders…
The Structure and Singularities of Arc Complexes
R. C. Penner
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 boun…
Surfaces, circles, and solenoids
R. C. Penner
Previous work of the author has developed coordinates on bundles over the classical Teichmueller spaces of punctured surfaces and on the space of cosets of the Moebius group in the…
The Weil-Petersson Kähler form and affine foliations on surfaces
Athanase Papadopoulos, R. C. Penner
The space of broken hyperbolic structures generalizes the Teichmüller space of a punctured surface, and the space of projectivized broken measured foliations (equivalently, the spa…
Cell decomposition and compactification of Riemann's moduli space in decorated Teichmüller theory
R. C. Penner
This survey covers earlier work of the author as well as recent work on Riemann's moduli space, its canonical cell decomposition and compactification, and the related operadic stru…
Decorated Teichmüller Theory of Bordered Surfaces
R. C. Penner
This paper extends the decorated Teichmüller theory developed before for punctured surfaces to the setting of ``bordered'' surfaces, i.e., surfaces with boundary, and there is non-…