Lagrangian traces for the Johnson filtration of the handlebody group

2022/06/21 by Quentin Faes, Faes, Quentin · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2206.10687

openalex publication_date 2022/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define trace-like operators on a subspace of the space of derivations of the free Lie algebra generated by the first homology group H of a surface Σ. This definition depends on the choice of a Lagrangian of H, and we call these operators the Lagrangian traces. We suppose that Σ is the boundary of a handlebody with first homology group H', and we show that the Lagrangian traces corresponding to the Lagrangian Ker (H → H') vanish on the image by the Johnson homomorphisms of the elements of the Johnson filtration that extend to the handlebody.

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• A Parametrization of Integral Homology 3-Spheres by the Fourth Johnson subgroup

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