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arXiv · 2206.10687

Lagrangian traces for the Johnson filtration of the handlebody group

Quentin Faes
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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 \emph{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 $\operatorname{Ker} (H \rightarrow H')$ vanish on the image by the Johnson homomorphisms of the elements of the Johnson filtration that extend to the handlebody.

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Quentin Faes. 2022-06-21. Lagrangian traces for the Johnson filtration of the handlebody group. https://arxiv.org/abs/2206.10687

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