Heegaard Floer knot trace invariants, exotic 4-manifolds, and symplectic obstructions

Abstract

We show that the numerical invariants $\nu$ and $|\varepsilon|$ 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 $\widehat{\nu}(K)=|\varepsilon(K)|(2\nu(K)-1)$, we give a new topological obstruction to a $4$-manifold being a strong symplectic filling of any contact structure on the boundary.