Bordered theory for pillowcase homology

Artem Kotelskiy (Princeton)

Pillowcase homology is a geometric construction, which was developed in order to better understand and compute a knot invariant called singular instanton knot homology. We will describe an algebraic extension of pillowcase homology. First we will associate an algebra A to the pillowcase. Then to an immersed curve L inside the pillowcase we will associate an A∞ module M(L) over A. Then we will show how, using these modules and a certain type DD structure, one can recover and compute Lagrangian Floer homology for immersed curves.