Categorification of the virtual braid groups

Anne-Laure Thiel

Displaying similar documents to “Categorification of the virtual braid groups”

Ribbon knots of 1-fusion, the Jones polynomial, and the Casson-Walker invariant.

Yoko Mizuma (2005)

Revista Matemática Complutense

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We give an explicit formula for the Casson-Walker invariant of double branched covers of S branched along ribbon knots of 1-fusion.

Basic results on braid groups

Juan González-Meneses (2011)

Annales mathématiques Blaise Pascal

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These are Lecture Notes of a course given by the author at the French-Spanish School , held in Pau (France) in October 2009. It is basically an introduction to distinct approaches and techniques that can be used to show results in braid groups. Using these techniques we provide several proofs of well known results in braid groups, namely the correctness of Artin’s presentation, that the braid group is torsion free, or that its center is generated by the full twist. We also recall some...

On three-dimensional space groups.

Conway, John H., Delgado Friedrichs, Olaf, Huson, Daniel H., Thurston, William P. (2001)

Beiträge zur Algebra und Geometrie

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The Knot Spectrum of Confined Random Equilateral Polygons

Y. Diao, C. Ernst, A. Montemayor, E. Rawdon, U. Ziegler (2014)

Molecular Based Mathematical Biology

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It is well known that genomic materials (long DNA chains) of living organisms are often packed compactly under extreme confining conditions using macromolecular self-assembly processes but the general DNA packing mechanism remains an unsolved problem. It has been proposed that the topology of the packed DNA may be used to study the DNA packing mechanism. For example, in the case of (mutant) bacteriophage P4, DNA molecules packed inside the bacteriophage head are considered to be circular...

On a multiplicativity up to homotopy of the Gugenheim map.

Kharebava, Z. (2002)

Georgian Mathematical Journal

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Obstructions to the section problem in a fibration with a weak formal base.

Saneblidze, S. (1997)

Georgian Mathematical Journal

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Braid Monodromy of Algebraic Curves

José Ignacio Cogolludo-Agustín (2011)

Annales mathématiques Blaise Pascal

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These are the notes from a one-week course on Braid Monodromy of Algebraic Curves given at the Université de Pau et des Pays de l’Adour during the Première Ecole Franco-Espagnole: Groupes de tresses et topologie en petite dimension in October 2009. This is intended to be an introductory survey through which we hope we can briefly outline the power of the concept monodromy as a common area for group theory, algebraic geometry, and topology of projective...

On the generalized Massey–Rolfsen invariant for link maps

A. Skopenkov (2000)

Fundamenta Mathematicae

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For $K = K_{1} ⊔ . . . ⊔ K_{s}$ and a link map $f : K \to ℝ^{m}$ let $K^{\sim} = ⊔_{i < j} K_{i} \times K_{j}$ , define a map $f^{\sim} : K^{\sim} \to S^{m - 1}$ by $f^{\sim} (x, y) = (f x - f y) / | f x - f y |$ and a (generalized) Massey-Rolfsen invariant $α (f) \in π^{m - 1} (K)$ to be the homotopy class of $f^{\sim}$ . We prove that for a polyhedron K of dimension ≤ m - 2 under certain (weakened metastable) dimension restrictions, α is an onto or a 1 - 1 map from the set of link maps $f : K \to ℝ^{m}$ up to link concordance to $π^{m - 1} (K^{\sim})$ . If $K_{1}, . . ., K_{s}$ are closed highly homologically connected manifolds of dimension $p_{1}, . . ., p_{s}$ (in particular, homology spheres), then $π^{m - 1} (K^{\sim}) ≅ \oplus_{i < j} π_{p_{i} + p_{j} - m + 1}^{S}$ .