Twist spun knots of twist spun knots of classical knots

Mizuki Fukuda; Masaharu Ishikawa

paper

Twist spun knots of twist spun knots of classical knots

arXiv:2409.00650

Abstract

A $k$ -twist spun knot is an $n + 1$ -dimensional knot in the $n + 3$ -dimensional sphere which is obtained from an $n$ -dimensional knot in the $n + 2$ -dimensional sphere by applying an operation called a $k$ -twist-spinning. This construction was introduced by Zeeman in 1965. In this paper, we show that the $m_{2}$ -twist-spinning of the $m_{1}$ -twist-spinning of a classical knot is a trivial $3$ -knot in $S^{5}$ if $g cd (m_{1}, m_{2}) = 1$ . We also give a sufficient condition for the $m_{2}$ -twist-spinning of the $m_{1}$ -twist-spinning of a classical knot to be non-trivial.

9 pages, 3 figures