Detecting Fibered Strongly Quasi-Positive Links

Abstract

Abstract We prove that an n-component fibered link L in S3 is strongly quasi-positive if and only if $\tau(L)=g_3(L)+n-1$, where $g_3(L)$ denotes the Seifert genus and τ is the Ozsváth–Szabó concordance invariant. We also provide a table which contains a list of some fibered prime links with at most 9 crossings; and we explicitly determine the ones that are strongly quasi-positive and their maximal self-linking number.