Strongly $n$-trivial Links are Boundary Links

Abstract

A link is said to be {\it strongly $n$-trivial} if there exists a diagram such that one can choose $n+1$ crossing points with the property that changing crossings on any $0 < m \le n+1$ points of these $n+1$ points yields a trivial link. It is shown that for a positive integer $n$ the components of a strongly $n$-trivial link admit mutually disjoint Seifert surfaces.