Filtered screens and augmented Teichmüller space
arXiv:1112.3915 · doi:10.1007/s10711-015-0083-7
Abstract
We study a new bordification of the decorated Teichmüller space for a multiply punctured surface F by a space of filtered screens on the surface that arises from a natural elaboration of earlier work of McShane-Penner. We identify necessary and sufficient conditions for paths in this space of filtered screens to yield short curves having vanishing length in the underlying surface F. As a result, an appropriate quotient of this space of filtered screens on F yields a decorated augmented Teichmüller space which is shown to admit a CW decomposition that naturally projects to the augmented Teichmüller space by forgetting decorations and whose strata are indexed by a new object termed partially oriented stratum graphs.
Final version to appear in Geometriae Dedicata