The pro-nilpotent Lawrence-Krammer-Bigelow representation
arXiv:2211.01855 · doi:10.1016/j.jpaa.2025.107952
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.
35 pages, 7 figures. Final version, to appear in Journal of Pure and Applied Algebra
References in corpus (8)
- A note on the Lawrence-Krammer-Bigelow representation
- Topological representations of motion groups and mapping class groups -- a unified functorial construction
- On p-almost direct products and residual properties of pure braid groups of nonorientable surfaces
- A family of representations of braid groups on surfaces
- A homological definition of the HOMFLY polynomial
- Point-pushing actions for manifolds with boundary
- When the lower central series stops: a comprehensive study for braid groups and their relatives
- Polynomiality of surface braid and mapping class group representations