An almost-integral universal Vassiliev invariant of knots.
An analogue of covering space theory for ranked posets.
An analytic interpretation of real dimension subgroups.
An approach to automorphisms of free groups and braids via transvections.
An asymptotic formula for the eta invariants of hyperbolic 3-manifolds.
An effective algorithm to get linking numbers of the 3-manifolds.
An elementary approach to the mapping class group of a surface.
An equivalence criterion for 3-manifolds.
Within geometric topology of 3-manifolds (with or without boundary), a representation theory exists, which makes use of 4-coloured graphs. Aim of this paper is to translate the homeomorphism problem for the represented manifolds into an equivalence problem for 4-coloured graphs, by means of a finite number of graph-moves, called dipole moves. Moreover, interesting consequences are obtained, which are related with the same problem in the n-dimensional setting.
An Exact Sequence of Braid Groups.
An expansion of the Jones representation of genus 2 and the Torelli group.
An extension of the Loop theorem and resolutions of generalized 3-manifolds with 0-dimensional singular set.
An implementation of the Bestvina-Handel algorithm for surface homeomorphisms.
An indecomposable -complex. II.
An infinite torus braid yields a categorified Jones-Wenzl projector
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.
An infinite-dimensional torsion-free FP...group.
An introduction to the abelian Reidemeister torsion of three-dimensional manifolds
These notes accompany some lectures given at the autumn school “Tresses in Pau” in October 2009. The abelian Reidemeister torsion for -manifolds, and its refinements by Turaev, are introduced. Some applications, including relations between the Reidemeister torsion and other classical invariants, are surveyed.
An invariant of link cobordisms from Khovanov homology.
An invariant of tangle cobordisms via subquotients of arc rings
We construct an explicit categorification of the action of tangles on tensor powers of the fundamental representation of quantum sl(2).
An irreducible Heegaard diagram of the real projective 3-space .
An obstruction to sliceness via contact geometry and "classical" gauge theory.