Bordered theory for pillowcase homology
Geometric Topology
2019-08-23 v2 Symplectic Geometry
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.
Cite
@article{arxiv.1707.07481,
title = {Bordered theory for pillowcase homology},
author = {Artem Kotelskiy},
journal= {arXiv preprint arXiv:1707.07481},
year = {2019}
}
Comments
Incorporated referee suggestions and other minor modifications; to appear in Mathematical Research Letters