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Geometry and Topology Seminar

Friday, September 30, 2022
4:00pm to 5:00pm
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Linde Hall 187
A filtered mapping cone formula for cables of the knot meridian
Hugo Zhou, School of Mathematics, Georgia Institute of Technology,

We construct a filtered mapping cone formula that computes the knot Floer complex of the (n,1)-cable of the knot meridian in any rational surgery, generalizing Truong's result about the (n,1)-cable of the knot meridian in large surgery and Hedden-Levine's filtered mapping cone formula. As an application, we show that there exist knots in integer homology spheres with arbitrary $\varphi_{i,j}$ values for any i>j>0, where $\varphi_{i,j}$ are the concordance homomorphisms defined by Dai-Hom-Stoffregen-Truong.

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