Complete invariant geodesic metrics on outer spaces and Jacobian varieties of tropical curves

2012/11/08 by Lizhen Ji, Ji, Lizhen · 1 citation
Mathematics · #20F28 #20F65 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1211.1995

openalex publication_date 2012/11/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let Out(F_n) be the outer automorphism group of the free group F_n. It acts properly on the outer space X_n of marked metric graphs, which is a finite-dimensional infinite simplicial complex with some simplicial faces missing. In this paper, we construct complete geodesic metrics and complete piecewise smooth Riemannian metrics on X_n which are invariant under Out(F_n). One key ingredient is the identification of metric graphs with tropical curves and the use of the tropical Jacobian map from the moduli space of tropical curves to the moduli space of principally polarized tropical abelian varieties.

Citations

• Moduli spaces of rational tropical curves
• Asymmetry of Outer Space

Cited by

• Metric Graph Kernels via the Tropical Torelli Map

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