9 citations · 12 across the 6 of their papers we have counts for
7 papers
On kernels of homological representations of mapping class groups
Renaud Detcherry, Jules Martel
We study the kernels of representations of mapping class groups of surfaces on twisted homologies of configuration spaces. We relate them with the kernel of a natural twisted inter…
Homological Construction of Quantum Representations of Mapping Class Groups
Marco De Renzi, Jules Martel
We provide a homological model for a family of quantum representations of mapping class groups arising from non-semisimple TQFTs (Topological Quantum Field Theories). Our approach…
Unified invariant of knots from homological braid action on Verma modules
Jules Martel, Sonny Willetts
We re-build the quantum sl2 unified invariant of knots from braid groups' action on tensors of Verma modules. It is a two variables series having the particularity of…
Colored Jones polynomials and abelianized Lefschetz numbers
Jules Martel
We show that the family of colored Jones polynomials of the closure of a braid compute weighted sums of abelianized Lefschetz numbers associated with the action of the braid on con…
The non semi-simple TQFT of the sphere with four punctures
Jules Martel
In this work, we compute the representation of the mapping class group of the sphere with punctures arising from the non semi-simple TQFT (constructed by Blanchet--Costantino--…
Colored version for Lawrence representations
Jules Martel
We give an explicit isomorphism between the Gassner representation and the first weight level of a representation of quantum sl(2). Then we construct and provide matrices for color…
A homological model for Verma-modules and their braid representations
Jules Martel
We extend Lawrence's representations of the braid groups to relative homology modules, and we show that they are free modules over a Laurent polynomials ring. We define homological…