Neck-Pinching of $CP^1$-structures in the $PSL(2,C)$-character variety
| Autor: | Baba, Shinpei |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We characterize a certain neck-pinching degeneration of (marked) $CP^1$- structures on a closed oriented surface S of genus at least two. Namely, we consider a path $C_t$ of $CP^1$-structures on S leaving every compact subset in the deformation space of (marked) $CP^1$-structures on S, such that its holonomy converges in the PSL(2, C)-character variety. In this setting, it is known that the complex structure $X_t$ of $C_t$ also leaves every compact subset in the Teichm\"uller space. In this paper, under the assumption that $X_t$ is pinched along a single loop m, we describe the limit of $C_t$ in terms of the developing maps, holomorphic quadratic differentials, and pleated surfaces. Moreover, we give an example of such a path $C_t$ whose limit holonomy is the trivial representation in the character variety. Comment: To appear in Journal of Topology; 66 pages, 24 figures |
| Databáze: | arXiv |
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