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math.GR2022
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…
math.GT2022
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…
math.GT2022★ 2 cited
When the lower central series stops: a comprehensive study for braid groups and their relatives
Jacques Darné, Martin Palmer, Arthur Soulié
Understanding the lower central series of a group is, in general, a difficult task. It is, however, a rewarding one: computing the lower central series and the associated Lie algeb…