2019/06/28 by Shinpei Baba, Baba, Shinpei
Mathematics · #Geometric and Algebraic Topology #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.1907.00092
We characterize a certain neck-pinching degeneration of (marked) CP1- structures on a closed oriented surface S of genus at least two. Namely, we consider a path Ct of CP1-structures on S leaving every compact subset in the deformation space of (marked) CP1-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 Xt of Ct also leaves every compact subset in the Teichmüller space. In this paper, under the assumption that Xt is pinched along a single loop m, we describe the limit of Ct in terms of the developing maps, holomorphic quadratic differentials, and pleated surfaces. Moreover, we give an example of such a path Ct whose limit holonomy is the trivial representation in the character variety.