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Tame and relatively
elliptic $\mathbb{CP}^1$–structures on the thrice-punctured
sphere
Samuel A Ballas, Philip L Bowers, Alex Casella and Lorenzo Ruffoni |
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Algebraic & Geometric Topology 24 (2024) 4589–4650
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Abstract |
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Suppose a relatively elliptic representation of the fundamental group of the thrice-punctured sphere is given. We prove that all projective structures on with holonomy and satisfying a tameness condition at the punctures can be obtained by grafting certain circular triangles. The specific collection of triangles is determined by a natural framing of . In the process, we show that (on a general surface of negative Euler characteristics) structures satisfying these conditions can be characterized in terms of their Möbius completion, and in terms of certain meromorphic quadratic differentials. |
Keywords
complex projective structure, configuration of circles,
grafting, Möbius completion, quadratic differential,
relatively elliptic representation, triangle group
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Mathematical Subject Classification
Primary: 30F30, 57M50
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References |
Publication
Received: 23 October 2022
Revised: 16 May 2023
Accepted: 14 June 2023
Published: 17 December 2024
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Authors |
| Samuel A Ballas | |
| Department of Mathematics Florida State University Tallahassee, FL United States |
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| Philip L Bowers | |
| Department of Mathematics Florida State University Tallahassee, FL United States |
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| Alex Casella | |
| Department of Mathematics Florida State University Tallahassee, FL United States |
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| Lorenzo Ruffoni | |
| Department of Mathematics Tufts University Medford, MA United States |
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| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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