Alexander invariants of ribbon tangles and planar algebras

@article{Damiani2018AlexanderIO,
  title={Alexander invariants of ribbon tangles and planar algebras},
  author={Celeste Damiani and Vincent F. B. Florens},
  journal={Journal of the Mathematical Society of Japan},
  year={2018}
}
  • C. Damiani, V. Florens
  • Published 19 February 2016
  • Mathematics
  • Journal of the Mathematical Society of Japan
Ribbon tangles are proper embeddings of tori and cylinders in the $4$-ball~$B^4$, "bounding" $3$-manifolds with only ribbon disks as singularities. We construct an Alexander invariant $\mathsf{A}$ of ribbon tangles equipped with a representation of the fundamental group of their exterior in a free abelian group $G$. This invariant induces a functor in a certain category $\mathsf{R}ib_G$ of tangles, which restricts to the exterior powers of Burau-Gassner representation for ribbon braids, that… 

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