On the Upsilon invariant of cable knots

Wenzhao Chen

Published 2016-04-16Version 1

In this paper, we study the behavior of $\Upsilon_K(t)$ under the cabling operation, where $\Upsilon_K(t)$ is the knot concordance invariant defined by Ozsv\'ath, Stipsicz, and Szab\'o, associated to a knot $K\subset S^3$. The main result is an inequality relating $\Upsilon_K(t)$ and $\Upsilon_{K_{p,q}}(t)$, which generalizes the inequalities of Hedden \cite{3} and Van Cott \cite{17} on the Ozsv\'ath-Szab\'o $\tau$-invariant.