Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Neck-Pinching of $CP^1$-structures in the $PSL(2,C)$-character variety (1907.00092v7)

Published 28 Jun 2019 in math.GT and math.DG

Abstract: 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 $C_t$ 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 $X_t$ 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.

Summary

We haven't generated a summary for this paper yet.