Cappell-Shaneson knot pairs with the same Alexander polynomial

Hisaaki Endo; Kazunori Iwaki; Andrei Pajitnov

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arXiv · 2604.01045

Cappell-Shaneson knot pairs with the same Alexander polynomial

Hisaaki Endo·Kazunori Iwaki·Andrei Pajitnov

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Abstract

It is well known that for $m\geq 2$ there are at most two non-equivalent $m$-knots with diffeomorphic exterior. Such pair of knots will be called $\textit{ non-reflexive knot pair}$. A classical problem in topology is to determine all dimensions where such knot pairs exist. In 1976 Cappell and Shaneson gave a method of constructing non-reflexive knot pairs. In the present paper we construct an infinite family of new examples of Cappell-Shaneson knot pairs, and give examples of Cappell-Shaneson knot pairs that have the same Alexander polynomial but are inequivalent.

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BibTeX RIS

Hisaaki Endo, Kazunori Iwaki, Andrei Pajitnov. 2026-04-01. Cappell-Shaneson knot pairs with the same Alexander polynomial. https://arxiv.org/abs/2604.01045

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