The Fukaya category of the pillowcase, traceless character varieties, and Khovanov cohomology

  title={The Fukaya category of the pillowcase, traceless character varieties, and Khovanov cohomology},
  author={Matthew Hedden and Christopher Herald and Matthew Hogancamp and Paul A. Kirk},
  journal={arXiv: Geometric Topology},
For a diagram of a 2-stranded tangle in the 3-ball we define a twisted complex of compact Lagrangians in the triangulated envelope of the Fukaya category of the smooth locus of the pillowcase. We show that this twisted complex is a functorial invariant of the isotopy class of the tangle, and that it provides a factorization of Bar-Natan's functor from the tangle cobordism category to chain complexes. In particular, the hom set of our invariant with a particular non-compact Lagrangian associated… 
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    Indiana University Mathematics Journal
  • 2021
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