Skip Navigation



Journal of Topology Advance Access published online on May 12, 2008
Journal of Topology, doi:10.1112/jtopol/jtn006
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
1/3/527    most recent
jtn006v1
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Penner, R. C.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2008 London Mathematical Society

The structure and singularities of quotient arc complexes

R. C. Penner

Departments of Mathematics and Physics/Astronomy, University of Southern California, Los Angeles, CA 90089, USA
Center for the Topology and Quantization of Moduli Spaces, Department of Mathematics, Aarhus University, DK-8000 Aarhus C, Denmark rpenner@math.usc.edu


  Abstract

A well-known 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 QA(F) consisting of equivalence classes of arcs in F connecting a given finite set of points in its boundary modulo diffeomorphisms of F pointwise fixing the boundary and any punctures. The main result of this paper is the determination of those complexes QA(F) that are also spheres. This classification has consequences for Riemann's moduli space of curves via its known identification with a related quotient arc complex in the punctured case with no boundary. Namely, the essential singularities of the natural cellular compactification of Riemann's moduli space can be described.

Received April 6, 2007.

2000 Mathematics Subject Classification 32G15, 57M99 (primary)


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.