On spherical surfaces of genus 1 with 1 conical point

Abstract: A spherical metric on a surface is a metric of constant curvature 1. Such a metric has a conical point x of angle $2\pi\theta$ if it has vanishing order $(\theta-1)$ at x. A spherical metric in an assigned conformal class can be viewed on one hand as a solution of a suitable singular Liouville equation. On the other hand, when the conformal class is not prescribed, isotopy classes of spherical metrics can be considered as flat (SO(3,R),S^2)-structure, and so their moduli space has a natural finite-dimensional real-analytic structure.

I will discuss recent results on the topology of such moduli space of spherical metrics with conical points of assigned angles. I will then focus on the case of genus 1 with 1 conical point.

This is joint work with Eremenko-Panov and with Eremenko-Gabrielov-Panov.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

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CRM - Séminaire du CIRGET / Géométrie et Topologie

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