Torus knots and generalized Schröder paths by Marko Stošić, Piotr Sułkowski

“…The lattice paths of our interest explicitly enumerate BPS states associated to knots via brane constructions, as well as encode 3-dimensional N=2 theories.…”
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Floer homology and non-fibered knot detection by John A. Baldwin, Steven Sivek

“…We prove for the first time that knot Floer homology and Khovanov homology can detect non-fibered knots and that HOMFLY homology detects infinitely many knots; these theories were previously known to detect a mere six knots, all fibered. …”
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The Toulouse–Kleman homotopic classification of topological defects in ordered systems illustrated by experiments by Pieranski, Pawel, Godinho, Maria Helena

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Towards Noncommutative Linking Numbers via the Seiberg-Witten Map by H. García-Compeán, O. Obregón, R. Santos-Silva

“…In the abelian Chern-Simons theory on a three-dimensional manifold, it is shown that the effect of noncommutativity is the appearance of 6n new knots at the nth order of the Seiberg-Witten expansion. …”
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