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math.GT2025
On the detection of knots by their traces in high dimensions
Valentina Bais, Alessio Di Prisa, Daniel Hartman +8
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 l…
math.GT2025
Pseudo-Isotopy and Diffeomorphisms of the 4-Sphere I: Loops of Spheres
David Gabai, David T. Gay, Daniel Hartman
We introduce new methods in pseudo-isotopy and embedding space theory. As an application we introduce an invariant that detects nontrivial loops of embedded 2-spheres in $S^{2} \ti…