Intersection of holonomy varieties of CP¹-structures

2025/02/17 by Baba, Shinpei
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2502.11322

Abstract

Let Σ be a closed orientable surface of genus at least two, and let X, Y be distinct marked Riemann surface structures on Σ, possibly with opposite orientations. In this paper, we show that there are (exactly) countably infinite pairs of \rm CP¹-structures on X and on Y sharing holonomy π₁(Σ) → \rm PSL₂ \rm C.

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