Filtered screens and augmented Teichmüller space
| Autor: | Douglas J. LaFountain, R. C. Penner |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Teichmüller space
Pure mathematics Mathematics::Dynamical Systems Mathematics::Complex Variables Riemann surface Hyperbolic geometry Space (mathematics) Surface (topology) Mathematics::Geometric Topology symbols.namesake Mathematics - Geometric Topology Mathematics - Algebraic Geometry Differential geometry symbols Geometry and Topology Quotient Mathematics Projective geometry |
| Popis: | 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. Comment: Final version to appear in Geometriae Dedicata |
| Databáze: | OpenAIRE |
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