On the detection of knotted spheres by their traces in high dimensions

Valentina Bais; Alessio Di Prisa; Daniel Hartman; Chun-Sheng Hsueh; Marc Kegel; Alice Merz; Mark Pencovitch; Arunima Ray; Diego Santoro; Paula Truöl; Laura Wakelin

arXiv · 2511.07251

On the detection of knotted spheres by their traces in high dimensions

Valentina Bais·Alessio Di Prisa·Daniel Hartman·Chun-Sheng Hsueh·Marc Kegel·Alice Merz·Mark Pencovitch·Arunima Ray·Diego Santoro·Paula Truöl·Laura Wakelin

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Abstract

For every $n \geq 4$, we demonstrate the existence of non-isotopic smooth $(n-2)$-knots in $S^n$ with diffeomorphic traces by generalising the RBG link construction to all dimensions. Conversely, we prove that for every $n \geq 4$, the unknot in $S^n$ is detected by the diffeomorphism type of its surgery and hence by its trace.

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Valentina Bais, Alessio Di Prisa, Daniel Hartman, Chun-Sheng Hsueh, Marc Kegel, Alice Merz, Mark Pencovitch, Arunima Ray, Diego Santoro, Paula Truöl, Laura Wakelin. 2025-11-10. On the detection of knotted spheres by their traces in high dimensions. https://arxiv.org/abs/2511.07251

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