学術雑誌論文

学術雑誌論文

Journal of Topology. 2025, 18(1), p. e70010

Neck-pinching of ℂP¹-structures in the PSL₂ℂ-character variety

Baba, Shinpei

John Wiley and Sons Ltd

英語

2025-03-01

https://doi.org/10.1112/topo.70010

Baba S. Neck-pinching of ℂP¹-structures in the PSL₂ℂ-character variety. Journal of Topology 18, e70010 (2025); https://doi.org/10.1112/topo.70010.

We characterize a certain neck-pinching degeneration of (marked) ℂP¹-structures on a closed oriented surface 𝑆 of genus at least two. In a more general setting, we take a path of ℂP¹-structures 𝐶ₜ (𝑡 ⩾ 0) on 𝑆 that leaves every compact subset in its deformation space, such that the holonomy of 𝐶ₜ converges in the PSL₂ℂ- character variety as 𝑡 →∞. Then, it is well known that the complex structure 𝑋ₜ of 𝐶ₜ also leaves every compact subset in the Teichmüller space of 𝑆. In this paper, under an additional assumption that 𝑋ₜ is pinched along a loop 𝑚 on 𝑆, we describe the limit of 𝐶ₜ from different perspectives: namely, in terms of the developing maps, holomorphic quadratic differentials, and pleated surfaces. The holonomy representations of ℂP¹-structures on 𝑆 are known to be nonelementary (i.e., strongly irreducible and unbounded). We also give a rather exotic example of such a path 𝐶ₜ whose limit holonomy is the trivial representation.

This article is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

100195

Neck-pinching of ℂP¹-structures in the PSL₂ℂ-character variety

Baba, Shinpei

John Wiley and Sons Ltd

英語

2025-03-01

Journal of Topology

18

1

e70010

https://doi.org/10.1112/topo.70010

https://hdl.handle.net/11094/100195