• Corpus ID: 126761466

Bordered invariants in low-dimensional topology.

@inproceedings{Kotelskiy2018BorderedII,
  title={Bordered invariants in low-dimensional topology.},
  author={Artem Kotelskiy},
  year={2018}
}
In this thesis we present two projects. In the first project, which covers Chapters 2 and 3, we construct an algebraic version of Lagrangian Floer homology for immersed curves in a surface with boundary. We first associate to the surface an algebra A1. Then to an immersed curve L inside the surface we associate an A∞ module M(L) over A1. Then we prove that Lagrangian Floer homology HF∗(L0, L1) is isomorphic to a suitable algebraic pairing of modules M(L0) and M(L1). We apply this theory to the… 
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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