Masatoshi Sato

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math.GT2026

On the Sp-structure of the torsion of the Lie algebra of homology cylinders

Quentin Faes, Gwenael Massuyeau, Masatoshi Sato

Let $Σ$ be a compact oriented surface. We investigate the graded Lie algebra of homology cylinders over $Σ$ , as introduced by M. Goussarov and K. Habiro. To analyze its torsion, we…

math.GT2024

Torsion elements in the associated graded of the $Y$ -filtration of the monoid of homology cylinders

Yuta Nozaki, Masatoshi Sato, Masaaki Suzuki

Clasper surgery induces the $Y$ -filtration ${Y_{n} I C}_{n}$ over the monoid of homology cylinders, which serves as a $3$ -dimensional analogue of the lower central series of…

math.GT2024

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 $⨁_{k \geq 1} Γ_{k} I / Γ_{k + 1} I$ of the lower central series $\mathcal{I} = Γ_1 \mathcal{I} \supset Γ_2 \mathcal{I} \s…

On the Sp-structure of the torsion of the Lie algebra of homology cylinders

Torsion elements in the associated graded of the Y-filtration of the monoid of homology cylinders

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

Torsion elements in the associated graded of the $Y$ -filtration of the monoid of homology cylinders