Year: 2024
Type: article
Abstract: Suppose a relatively elliptic representation of the fundamental group of the thrice-punctured sphere S is given.We prove that all projective structures on S 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.30F30, 57M50 1. Introduction 4589 2. Basics on complex projective geometry 4596 3. Tame and relatively elliptic CP 1 -structures 4612 4. The complex analytic point of view 4632 5. Structures on the thrice-punctured sphere 4636 Appendix.Tables of atomic triangular immersions 4646
Source: Algebraic & Geometric Topology
Institutions: Florida State University, Tufts University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4405637600