Bordered theory for pillowcase homology

@article{Kotelskiy2019BorderedTF,
  title={Bordered theory for pillowcase homology},
  author={Artem Kotelskiy},
  journal={Mathematical Research Letters},
  year={2019}
}
  • Artem Kotelskiy
  • Published 24 July 2017
  • Mathematics
  • Mathematical Research Letters
We construct an algebraic version of Lagrangian Floer homology for immersed curves inside the pillowcase. We first associate to the pillowcase an algebra A. Then to an immersed curve L inside the pillowcase we associate an A infinity module M(L) over A. Then we prove that Lagrangian Floer homology HF(L,L') is isomorphic to a suitable algebraic pairing of modules M(L) and M(L'). This extends the pillowcase homology construction - given a 2-stranded tangle inside a 3-ball, if one obtains an… 
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The Fukaya category of the pillowcase, traceless character varieties, and Khovanov Cohomology
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…

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