Title : On strongly $n$-trivial links
Speaker : Ichiro Torisu (Akita University)
Abstract :

A $k$-component link $L$ in $S^3$ is {\it strongly n-trivial} if there exist $n+1$ crossings contained in a diagram of $L$ such that the result of any $0<m\leq n+1$ crossing changes on these crossings is the $k$-component trivial link. By definition, strongly n-trivial link is automatically strongly $(n-1)$-trivial. For knot case (ie. $k=1$), Howards--Luecke showed that the trivial knot is the only knot that is strongly $n$-trivial for all $n$. In fact, they proved that if $K$ is non-trivial and strongly $n$-trivial, then $n$ is less than $6g(K)-3$, where $g(K)$ is the genus of $K$. Also recently the speaker proved that a non-trivial $2$-bridge knot is strongly $1$-trivial only if it is the trefoil knot or figure-eight knot. In this talk, we will extend these results to link case.

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