HOMFLYPT homology for links in handlebodies via type A Soergel bimodules

@article{Rose2019HOMFLYPTHF,
  title={HOMFLYPT homology for links in handlebodies via type A Soergel bimodules},
  author={David E. V. Rose and Daniel Tubbenhauer},
  journal={arXiv: Quantum Algebra},
  year={2019}
}
We define a triply-graded invariant of links in a genus g handlebody, generalizing the colored HOMFLYPT (co)homology of links in the 3-ball. Our main tools are the description of these links in terms of a subgroup of the classical braid group, and a family of categorical actions built from complexes of (singular) Soergel bimodules. 
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