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| Format: | Preprint |
| Veröffentlicht: |
2011
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/1112.3915 |
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| _version_ | 1866916644654153728 |
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| author | LaFountain, Douglas J. Penner, R. C. |
| author_facet | LaFountain, Douglas J. Penner, R. C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1112_3915 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Filtered screens and augmented Teichmüller space LaFountain, Douglas J. Penner, R. C. Geometric Topology Algebraic Geometry 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. |
| title | Filtered screens and augmented Teichmüller space |
| topic | Geometric Topology Algebraic Geometry |
| url | https://arxiv.org/abs/1112.3915 |