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math.GT2025
Mutual arc presentations and braided open books
Benjamin Bode, Chun-Sheng Hsueh
We show that every canonically fibered link in is the binding of a braided open book in , addressing a question of Montesinos and Morton. We introduce mutual arc present…
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
Handle decompositions and stabilizations of open books
Chun-Sheng Hsueh
We build handle decompositions of n-manifolds that encode given open book decompositions and describe handle slides that reveal new open book decompositions on the same underlying…