Filtered screens and augmented Teichm\"uller space

Douglas J. LaFountain; R. C. Penner

doi:10.1007/s10711-015-0083-7

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arXiv · 1112.3915

Filtered screens and augmented Teichm\"uller space

Douglas J. LaFountain·R. C. Penner

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Abstract

We study a new bordification of the decorated Teichm\"uller 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 Teichm\"uller space which is shown to admit a CW decomposition that naturally projects to the augmented Teichm\"uller space by forgetting decorations and whose strata are indexed by a new object termed partially oriented stratum graphs.

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BibTeX RIS

Douglas J. LaFountain, R. C. Penner. 2011-12-16. Filtered screens and augmented Teichm\"uller space. https://doi.org/10.1007/s10711-015-0083-7

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