c-Gluing construction and slices of quasi-Fuchsian space
| Autor: | Sara Maloni |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Hyperbolic geometry
010102 general mathematics Holonomy 30F40 30F60 57M50 Sigma Geometric Topology (math.GT) Algebraic geometry Space (mathematics) Surface (topology) Mathematics::Geometric Topology 01 natural sciences Combinatorics Mathematics - Geometric Topology Differential geometry 0103 physical sciences FOS: Mathematics 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematics Projective geometry |
| Zdroj: | Geometriae Dedicata. 212:107-139 |
| ISSN: | 1572-9168 0046-5755 |
| DOI: | 10.1007/s10711-020-00551-5 |
| Popis: | Given a pants decomposition $\mathcal{PC} = \{\gamma_1, \ldots, \gamma_{\xi}\}$ on a hyperbolizable surface $\Sigma$ and a vector $\underline{c} = (c_1, \ldots, c_{\xi}) \in \mathbb{R}_+^\xi$, we describe a plumbing construction which endows $\Sigma$ with a complex projective structure for which the associated holonomy representation $\rho$ is quasi-Fuchsian and for which $\ell_\rho(\gamma_i) = c_i$. When $\underline{c} \to \underline{0} = (0, \ldots, 0)$ this construction limits to Kra's plumbing construction. In addition, when $\Sigma = \Sigma_{1,1}$, the holonomy representations of these structures belong to the `linear slice' of quasi-Fuchsian space $\mathrm{QF}(\Sigma)$ defined by Komori and Parkonnen. We discuss some conjectures for these slices suggested by the pictures we created in joint work with Yamashita. Comment: 27 pages, 10 figures |
| Databáze: | OpenAIRE |
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