On the detection of knotted spheres by their traces in high dimensions
Authors
Valentina Bais
Alessio Di Prisa
Daniel Hartman
Chun-Sheng Hsueh
Marc Kegel
Alice Merz
Mark Pencovitch
Arunima Ray
Diego Santoro
Paula Truöl
Laura Wakelin
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.
