Displaying similar documents to “Twisting in a Crowd”

An infinite torus braid yields a categorified Jones-Wenzl projector

Lev Rozansky (2014)

Fundamenta Mathematicae

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A sequence of Temperley-Lieb algebra elements corresponding to torus braids with growing twisting numbers converges to the Jones-Wenzl projector. We show that a sequence of categorification complexes of these braids also has a limit which may serve as a categorification of the Jones-Wenzl projector.

Pure virtual braids homotopic to the identity braid

H. A. Dye (2009)

Fundamenta Mathematicae

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Two virtual link diagrams are homotopic if one may be transformed into the other by a sequence of virtual Reidemeister moves, classical Reidemeister moves, and self crossing changes. We recall the pure virtual braid group. We then describe the set of pure virtual braids that are homotopic to the identity braid.

Braids and Signatures

Jean-Marc Gambaudo, Étienne Ghys (2005)

Bulletin de la Société Mathématique de France

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A braid defines a link which has a signature. This defines a map from the braid group to the integers which is not a homomorphism. We relate the homomorphism defect of this map to Meyer cocycle and Maslov class. We give some information about the global geometry of the gordian metric space.

Conjugacy for positive permutation braids

Hugh R. Morton, Richard J. Hadji (2005)

Fundamenta Mathematicae

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Positive permutation braids on n strings, which are defined to be positive n-braids where each pair of strings crosses at most once, form the elementary but non-trivial building blocks in many studies of conjugacy in the braid groups. We consider conjugacy among these elementary braids which close to knots, and show that those which close to the trivial knot or to the trefoil are all conjugate. All such n-braids with the maximum possible crossing number are also shown to be conjugate. ...