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We prove that each overtwisted contact structure has knot types that are represented by
infinitely many distinct transverse knots all with the same self-linking number. In some cases, we can even cla...
A new type of knot energy is presented via real life experiments involving a thin resilient metallic tube. Knotted in different ways, the device mechanically acquires a uniquely determined (up to iso...
An Injectivity Theorem for Casson-Gordon Type Representations relating to the Concordance of Knots and Links
Injectivity Theorem Casson-Gordon Type Representations Concordance of Knots and Links
2010/11/24
In the study of homology cobordisms, knot concordance and link concordance, the following technical problem arises frequently: let $\pi$ be a group and let $M \to N$ be a homomorphism between project...
A Functorial Map from Knots in Thickened Surfaces to Classical Knots and Generalisations of Parity
Functorial Map Thickened Surfaces Classical Knots
2010/11/24
We construct a functorial map from knots in thickened surfaces to classical knots. This method uses a natural generalisation of the notion of parity: we localise the information about non-triviality ...
Two Dehn surgeries on a knot are called purely cosmetic, if they yield manifolds that are homeomorphic as oriented manifolds. Using Heegaard Floer homology, we give necessary conditions for the existe...
In this paper, we introduce general formulas finding the Bracket polynomials of torus knot K (2, n) and Jones polynomials of torus knots K (2, n) .
An upper bound of the superbridge index of the connected sum of two knots is given in terms of the braid index of the summands. Using this upper bound and minimal polygonal presentations, we give an ...