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Operators and Correspondences in Heegaard Floer homology
Geometry/Topology| Speaker: | Jacob Rasmussen, University of Illinois |
| Related Webpage: | https://rasmusj.web.illinois.edu/ |
| Location: | 2112 MSB |
| Start time: | Thu, Feb 19 2026, 2:10PM |
Description
The bordered Floer homology of a 3-manifold with torus boundary can be interpreted as a collection of immersed curves in the punctured torus. Similarly, the bordered Floer homology of a 3-dimensional cobordism $M:T^2->T^2$ give an operator $F_M$ which eats an immersed curve on the punctured torus and spits out another such curve. (More formally, $F_M$ is a functor from the Fukaya category of the punctured torus to itself.) I'll explain how to describe some interesting examples (the cabling operator, for example) using correspondences, without ever having to compute their bordered Floer homology. I will also discuss some relations with mirror symmetry. Based on joint work with Holt Bodish and James Pascaleff.