Johnson's homomorphisms and the Arakelov-Green function

2008/01/28 by Nariya Kawazumi, Kawazumi, Nariya · 1 citation
Mathematics · #14H15 #32G15 (Secondary) #57R20 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.AG #math.GT #msc:14H15 #msc:32G15 #msc:57R20

paper · pdf · doi:10.48550/arxiv.0801.4218

arxiv created 2008/01/28 · openalex publication_date 2008/01/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let π: \mathbb C_g → \mathbb M_g be the universal family of compact Riemann surfaces of genus g ≥ 1. We introduce a real-valued function on the moduli space \mathbb M_g and compute the first and the second variations of the function. As a consequence we relate the Chern form of the relative tangent bundle T_\mathbb C_g/\mathbb M_g induced by the Arakelov-Green function with differential forms on \mathbb C_g induced by a flat connection whose holonomy gives Johnson's homomorphisms on the mapping class group.

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