4 citations · 8 across the 9 of their papers we have counts for
10 papers
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…
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…
Quantum Invariants of Ribbon Surfaces in -Dimensional -Handlebodies
Anna Beliakova, Marco De Renzi, Quentin Faes
We use unimodular ribbon categories to construct quantum invariants of ribbon surfaces in -dimensional -handlebodies up to -isotopy. In the process, we recover invariants…
Non-factorizable ribbon Hopf Algebras
Quentin Faes, Maksymilian Manko
Building on the work of Nenciu we provide examples of non-factorizable ribbon Hopf algebras, and introduce a stronger notion of non-factorizability. These algebras are designed to…
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 of the lower central series $\mathcal{I} = Γ_1 \mathcal{I} \supset Γ_2 \mathcal{I} \s…
About torsion in the cokernels of the Johnson homomorphisms
Quentin Faes
The so-called Johnson homomorphisms embed the graded space associated to the Johnson filtration of a surface with one boundary component into the Lie ring of pos…
On the non-triviality of the torsion subgroup of the abelianized Johnson kernel
Quentin Faes, Gwenael Massuyeau
The Johnson kernel is the subgroup of the mapping class group of a closed oriented surface that is generated by Dehn twists along separating simple closed curves. The rational abel…
Lagrangian traces for the Johnson filtration of the handlebody group
Quentin Faes
We define trace-like operators on a subspace of the space of derivations of the free Lie algebra generated by the first homology group of a surface . This definition depends…
Triviality of the -equivalence among homology 3-spheres
Quentin Faes
We prove that all homology 3-spheres are -equivalent, i.e. that any homology 3-sphere can be obtained from one another by twisting one of its Heegaard splittings by an element…
The handlebody group and the images of the second Johnson homomorphism
Quentin Faes
Given an oriented surface bounding a handlebody, we study the subgroup of its mapping class group defined as the intersection of the handlebody group and the second term of the Joh…