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Topology/Geometry Seminar

Bordered theory for pillowcase homology

Artem Kotelskiy, Princeton

Location:  Hill 525
Date & time: Tuesday, 14 November 2017 at 3:30PM - 4:30PM

Abstract:  Pillowcase homology is a geometric construction, which was developed in order to better understand and compute a knot invariant I(K) called singular instanton knot homology. Motivated by the problem of extending pillowcase homology to tangles, we will introduce the following construction. The pillowcase P is a torus factorized by hyperelliptic involution, and after removing 4 singular points one obtains a 4-punctured 2-sphere P*. First, we will associate an algebra A to the pillowcase P*. Second, to an immersed curve L inside P* we will associate an A? module M(L) over A. Then we will show how, using these modules, one can recover and compute Lagrangian Floer homology (i.e. geometric intersection number) for immersed curves.

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