4 papers
Twisted homological stability for handlebody mapping class groups
Erik Lindell, Arthur Soulié
We prove twisted homological stability for handlebody mapping class groups. Using the categorical framework developed by Randal-Williams and Wahl, we establish that the homology of…
The pro-nilpotent Lawrence-Krammer-Bigelow representation
Martin Palmer, Arthur Soulié
We construct a 3-variable enrichment of the Lawrence-Krammer-Bigelow (LKB) representation of the braid groups, which is the limit of a pro-nilpotent tower of representations having…
Polynomiality of surface braid and mapping class group representations
Martin Palmer, Arthur Soulié
We study a wide range of homologically-defined representations of surface braid groups and of mapping class groups of surfaces, including the Lawrence-Bigelow representations of th…
Stable twisted cohomology of the mapping class groups in the unit tangent bundle homology
Nariya Kawazumi, Arthur Soulié
We compute the stable cohomology groups of the mapping class groups of compact orientable surfaces with one boundary, with twisted coefficients given by the homology of the unit ta…