Results 1 to 10 of about 1,468 (49)
Primary decomposition in the smooth concordance group of topologically slice knots
Forum of Mathematics, Sigma, 2021 We address primary decomposition conjectures for knot concordance groups, which predict direct sum decompositions into primary parts. We show that the smooth concordance group of topologically slice knots has a large subgroup for which the conjectures ...
Jae Choon Cha
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On the torsional energy of torus knots under infinitesimal bending
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 The article deals with the infinitesimal bending theory application to the knots theory. The impact of infinitesimal bending on the torsional energy at torus knots is considered, and the results show that it is not stationary under infinitesimal bending.
Maksimović Miroslav D. +4 more
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Proceedings of the London Mathematical Society, Volume 121, Issue 4, Page 954-1032, October 2020., 2020 Abstract I provide an explicit construction of spectral curves for the affine E8 relativistic Toda chain. Their closed‐form expression is obtained by determining the full set of character relations in the representation ring of E8 for the exterior algebra of the adjoint representation; this is in turn employed to provide an explicit construction of ...
Andrea Brini
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$q$-DEFORMED RATIONALS AND $q$-CONTINUED FRACTIONS
Forum of Mathematics, Sigma, 2020 We introduce a notion of $q$-deformed rational numbers and $q$-deformed continued fractions. A $q$-deformed rational is encoded by a triangulation of a polygon and can be computed recursively. The recursive formula is analogous to the $q$-deformed Pascal
SOPHIE MORIER-GENOUD, VALENTIN OVSIENKO
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SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS
Forum of Mathematics, Sigma, 2019 We construct infinitely many compact, smooth 4-manifolds which are homotopy equivalent to $S^{2}$ but do not admit a spine (that is, a piecewise linear embedding of $S^{2}$ that realizes the homotopy equivalence).
ADAM SIMON LEVINE, TYE LIDMAN
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Bounds for the Thurston-Bennequin number from Floer homology [PDF]
, 2004 Using a knot concordance invariant from the Heegaard Floer theory of Ozsvath and Szabo, we obtain new bounds for the Thurston-Bennequin and rotation numbers of Legendrian knots in S^3.
Akbulut +3 more
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Introduction to disoriented knot theory
Open Mathematics, 2018 This paper is an introduction to disoriented knot theory, which is a generalization of the oriented knot and link diagrams and an exposition of new ideas and constructions, including the basic definitions and concepts such as disoriented knot ...
Altıntaş İsmet
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THE CONORMAL TORUS IS A COMPLETE KNOT INVARIANT
Forum of Mathematics, Pi, 2019 We use microlocal sheaf theory to show that knots can only have Legendrian isotopic conormal tori if they themselves are isotopic or mirror images.
VIVEK SHENDE
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Involutory biquandles and singular knots and links
Open Mathematics, 2018 We define a new algebraic structure for singular knots and links. It extends the notion of a bikei (or involutory biquandle) from regular knots and links to singular knots and links. We call this structure a singbikei.
Bataineh Khaled, Ghaith Hadeel
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NONSURJECTIVE SATELLITE OPERATORS AND PIECEWISE-LINEAR CONCORDANCE
Forum of Mathematics, Sigma, 2016 We exhibit a knot $P$ in the solid torus, representing a generator of first homology, such that for any knot
ADAM SIMON LEVINE
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