DOI: 10.1112/plms.70226 ISSN: 0024-6115

On the detection of knots 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 , we demonstrate the existence of non‐isotopic, smooth ‐knots in  with diffeomorphic traces. We give two proofs: the first by generalising the RBG link construction to all dimensions, and the second as an application of work of Plotnick. Conversely, we prove that for every , the unknot in is detected by the diffeomorphism type of its surgery and hence of its trace.

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