Filtered screens and augmented Teichmüller space

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.

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