Heegaard Floer knot trace invariants, exotic 4-manifolds, and symplectic obstructions
Jennifer Hom, Shunyu Wan
Abstract
We show that the numerical invariants ν and || coming from knot Floer homology are knot n-trace invariants for any integer n, resolving the remaining case in Hayden-Mark-Piccirillo. This extension allows us to construct new families of exotic pairs using Yasui patterns. Moreover, by studying the invariant ν(K)=|(K)|(2ν(K)-1), we give a new topological obstruction to a 4-manifold being a strong symplectic filling of any contact structure on the boundary.
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