Georgia Institute of Technology College of Sciences

For a genus g surface with s > 0 punctures and 2g+s > 2, decorated Teichmuller space (DTeich) is a trivial R_+^s-bundle over the usual Teichmuller space, where the fiber corresponds to families of horocycles peripheral to each puncture. As proved by R. Penner, DTeich admits a mapping class group-invariant cell decomposition, which then descends to a cell decomposition of Riemann's moduli space. In this talk we introduce a new cellular bordification of DTeich which is also MCG-invariant, namely the space of filtered screens. After an appropriate quotient, we obtain a cell decomposition for a new compactification of moduli space, which is shown to be homotopy equivalent to the Deligne-Mumford compactification. This work is joint with R. Penner.