The pro-nilpotent Lawrence-Krammer-Bigelow representation
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Abstract 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 the original LKB representation as its bottom layer. We also construct analogous pro-nilpotent towers of representations of surface braid groups and loop braid groups. |
This builds on (and is an application of) earlier joint work with Jacques Darné and Arthur Soulié on the lower central series of braid groups and their relatives. |