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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 be a compact oriented surface. We investigate the graded Lie algebra of homology cylinders over , as introduced by M. Goussarov and K. Habiro. To analyze its torsion, we…
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 coincides with the kernel of Morita's trace map for the case of a surface of genus with one boundary…