Bordered theory for pillowcase homology

Artem Kotelskiy

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arXiv · 1707.07481

Bordered theory for pillowcase homology

Artem Kotelskiy

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Abstract

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 immersed unobstructed Lagrangian inside the pillowcase, one can further associate an A infinity module to that Lagrangian.

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Artem Kotelskiy. 2017-07-24. Bordered theory for pillowcase homology. https://arxiv.org/abs/1707.07481

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