3 papers
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.GT2024
The Alexander and Markov theorems for strongly involutive links
Alice Merz
The Alexander theorem (1923) and the Markov theorem (1936) are two classical results in knot theory that show respectively that every link is the closure of a braid and that braids…
math.GT2021
The homomorphism defect of an extended Levine-Tristram signature via twisted homology
Alice Merz
Taking the Levine-Tristram signature of the closure of a braid defines a map from the braid group to the integers. A formula of Gambaudo and Ghys provides an evaluation of the homo…