Geodesic
Tame and relatively elliptic ℂℙ1–structures on the thrice-punctured sphere
Ballas, Samuel A1 ; Bowers, Philip L1 ; Casella, Alex1 ; Ruffoni, Lorenzo2
1 Department of Mathematics, Florida State University, Tallahassee, FL, United States
2 Department of Mathematics, Tufts University, Medford, MA, United States
Algebraic and Geometric Topology, Tome 24 (2024) no. 8, pp. 4589-4650

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

Suppose a relatively elliptic representation ρ of the fundamental group of the thrice-punctured sphere S is given. We prove that all projective structures on S with holonomy ρ 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 ρ. In the process, we show that (on a general surface Σ 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.

DOI : 10.2140/agt.2024.24.4589
Keywords: complex projective structure, configuration of circles, grafting, Möbius completion, quadratic differential, relatively elliptic representation, triangle group

Ballas, Samuel A 1 ; Bowers, Philip L 1 ; Casella, Alex 1 ; Ruffoni, Lorenzo 2

1 Department of Mathematics, Florida State University, Tallahassee, FL, United States
2 Department of Mathematics, Tufts University, Medford, MA, United States 
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     title = {Tame and relatively elliptic {\ensuremath{\mathbb{C}}\ensuremath{\mathbb{P}}1{\textendash}structures} on the thrice-punctured sphere},
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Ballas, Samuel A; Bowers, Philip L; Casella, Alex; Ruffoni, Lorenzo. Tame and relatively elliptic ℂℙ1–structures on the thrice-punctured sphere. Algebraic and Geometric Topology, Tome 24 (2024) no. 8, pp. 4589-4650. doi: 10.2140/agt.2024.24.4589

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