Mathematics Colloquia and Seminars

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Bordered Heegaard Floer homology extends Heegaard Floer homology to 3–manifolds with boundary via a boundary algebra and module invariants, turning cutting/gluing into algebra and recovering the Heegaard Floer homology of the glued manifold. For torus boundary, the bordered invariant can be encoded by immersed curves so that gluing becomes Lagrangian Floer homology. I’ll use this immersed-curve perspective to analyze knot Floer properties of (1,1)-satellite knots. In particular, I’ll discuss rank inequalities for knot Floer homology and a geometric algorithm for computing torsion orders. This is based on both independent work and joint work with Wenzhao Chen.