Quentin Faes

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math.GT2026

Image of the third Johnson homomorphism

Quentin Faes, Ricard Riba

In this note we show that the image of the third Johnson homomorphism $τ_{3}$ coincides with the kernel of Morita's trace map for the case of a surface of genus $g$ with one boundary…

math.GT2025

Quantum Invariants of Ribbon Surfaces in $4$ -Dimensional $2$ -Handlebodies

Anna Beliakova, Marco De Renzi, Quentin Faes

We use unimodular ribbon categories to construct quantum invariants of ribbon surfaces in $4$ -dimensional $2$ -handlebodies up to $1$ -isotopy. In the process, we recover invariants…

math.GT2025

On the degree-two part of the associated graded of the lower central series of the Torelli group

Quentin Faes, Gwenael Massuyeau, Masatoshi Sato

We consider the associated graded $⨁_{k \geq 1} I^_{k} I / I^_{k + 1} I$ of the lower central series $\mathcal{I} = Î_1 \mathcal{I} \supset Î_2 \mathcal{I…

Image of the third Johnson homomorphism

Quantum Invariants of Ribbon Surfaces in 4-Dimensional 2-Handlebodies

On the degree-two part of the associated graded of the lower central series of the Torelli group

Quantum Invariants of Ribbon Surfaces in $4$ -Dimensional $2$ -Handlebodies