Behavior of knot invariants under genus 2 mutation.
Bipartite knots
We give a solution to a part of Problem 1.60 in Kirby's list of open problems in topology, thus answering in the positive the question raised in 1987 by J. Przytycki.
Boundary slopes (nearly) bound cyclic slopes.
Bounds for the Thurston-Bennequin number from Floer homology.
Brunnian local moves of knots and Vassiliev invariants
K. Habiro gave a neccesary and sufficient condition for knots to have the same Vassiliev invariants in terms of -moves. In this paper we give another geometric condition in terms of Brunnian local moves. The proof is simple and self-contained.
Burnside obstructions to the Montesinos-Nakanishi 3-move conjecture.
Calculus of clovers and finite type invariants of 3-manifolds.
Catégorification des coefficients de la matrice de la représentation de Burau
Nous catégorifions explicitement les coefficients de la matrice de la représentation de Burau en utilisant des méthodes géométriques élémentaires. Nous montrons que cette catégorification est fidèle dans le sens où elle détecte la tresse triviale.
Categorification of the Kauffman bracket skein module of -bundles over surfaces.
Categorification of the virtual braid groups
We extend Rouquier’s categorification of the braid groups by complexes of Soergel bimodules to the virtual braid groups.
Character varieties of mutative 3-manifolds.
Characters on the trivalent diagram algebra .
Chewing the Khovanov homology of tangles
We present an elementary description of Khovanov's homology of tangles [K2], in the spirit of Viro's paper [V]. The formulation here is over the polynomial ring ℤ[c], unlike [K2] where the theory was presented over the integers only.
Claspers and finite type invariants of links.
Classical and quantum dilogarithmic invariants of flat -bundles over 3-manifolds.
Clover calculus for homology 3-spheres via basic algebraic topology.
Cohomology rings, Rochlin function, linking pairing and the Goussarov-Habiro theory of three-manifolds.
Computations of the Ozsvath-Szabo knot concordance invariant.
Concordance and 1-loop clovers.
Concordance and mutation.