Piecewise circular curves and flag positivity.

Abstract: In this joint work with Ryan Kirk, we investigate moduli spaces of closed piecewise circular curves. A curve is piecewise circular if it is made of pieces which are circular arcs, and these arcs are tangent at the intersection of pieces. We identify a special connected component of these moduli spaces and prove that it is homeomorphic to an open ball of dimension 2n-10. We characterize this component as the subset of curves which have decreasing curvature in an appropriate sense. The proof involves "Lie circle geometry", a somewhat out of fashion theory of the homogeneous spaces of Sp(4,R), and Lusztig-Fock-Goncharov positivity.

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

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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