arXiv:2610.33280v1 Announce Type: new Abstract: For a null-homologous fibered knot $K$ in a rational homology sphere, Baldwin and Vela-Vick define a refinement $b(K)$ of the Ozsv\'ath-Szab\'o contact invariant. We prove that if the Ozsv\'ath-Stipsicz-Szab\'o concordance invariant Upsilon has slope $\Upsilon'_K(t)=-g(K)$ for some $t\in[0,\frac{2}{n+1})$, where $g(K)$ is the genus of $K$, then $b(K)>n$. This extends a result of He, Hubbard, and the author on the Upsilon invariant and right-veering monodromies. We also prove that the knot Floer homology of a fibered knot in the $g(K)-b(K)$ Alexander grading is nonvanishing. As an application, we give many families of fibered cable knots whose $b(K)$ invariant grows arbitrarily large. Finally, we prove that if a monodromy of a fibered knot is neither right-veering nor left-veering, then the third-to-top term of knot Floer homology is nonvanishing.
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