Outputs (4)

S-equivalence of knots (2004)
Journal Article
Kearton, C. (2004). S-equivalence of knots. Journal of Knot Theory and Its Ramifications, 13(06), 709-717. https://doi.org/10.1142/s0218216504003408

S-equivalence of classical knots is investigated, as well as its relationship with mutation and the unknotting number. Furthermore, we identify the kernel of Bredon's double suspension map, and give a geometric relation between slice and algebraicall... Read More about S-equivalence of knots.

Sharp bounds on some classical knot invariants (2003)
Journal Article
Kearton, C., & Wilson, S. (2003). Sharp bounds on some classical knot invariants. Journal of Knot Theory and Its Ramifications, 12(06), 805-817. https://doi.org/10.1142/s0218216503002792

There are obvious inequalities relating the Nakanishi index of a knot, the bridge number, the degree 2n of the Alexander polynomial and the length of the chain of Alexander ideals. We give examples for every positive value of n to show that these bou... Read More about Sharp bounds on some classical knot invariants.

Knot modules and the Nakanishi index (2003)
Journal Article
Kearton, C., & Wilson, S. (2003). Knot modules and the Nakanishi index. Proceedings of the American Mathematical Society, 131(2), 655-663

We examine the structure of the knot module of $9_{38}$ and show that the Nakanishi index of this knot is 2. The Nakanishi indices of $10_{69}$ and $10_{101}$ are also determined, by means of the Fox-Smythe row class. Finally, we point out that the N... Read More about Knot modules and the Nakanishi index.

Simple non-finite knots are not prime in higher dimensions (2003)
Journal Article
Kearton, C., & Wilson, S. (2003). Simple non-finite knots are not prime in higher dimensions. Journal of Knot Theory and Its Ramifications, 12(02), 225-241. https://doi.org/10.1142/s0218216503002408

It has long been known that in high dimensions tbere are examples of irreducible knots which are not prime. Here we show that in fact there are no prime simple knots in high dimensions, with the possible exception of those whose homology is finite. I... Read More about Simple non-finite knots are not prime in higher dimensions.