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articleNo Access
Knot adjacency from a surgical view of Alexander invariants
- Yasutaka Nakanishi and
- Masahiro Shimoda
Journal of Knot Theory and Its Ramifications01 Dec 2017
Preview Abstract
For two knots $K_{1}$ $K_{1}$ and $K_{2}$ $K_{2}$ , $K_{1}$ $K_{1}$ is said to be $n$ $n$ -adjacent to $K_{2}$ $K_{2}$ , if $K_{1}$ $K_{1}$ admits a knot diagram containing $n$ $n$ crossings such that crossing changes at any non-empty subset of them yield a knot diagram of $K_{2}$ $K_{2}$ . Using a surgical view of Alexander invariants, we will characterize the Alexander polynomials of knots which are $2$ $2$ -adjacent to the trivial knot.

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