English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The universal Vassiliev-Kontsevich invariant is a functor from the categoryof tangles to a certain graded category of chord diagrams, compatible with theVassiliev filtration and whose associated graded is an isomorphism. TheVassiliev filtration has a natural extension to tangles in any thickenedsurface $M\times I$ but the corresponding category of diagrams lacks somefiniteness properties which are essential to the above construction. We suggestto overcome this obstruction by studying families of Vassiliev invariantswhich, roughly, are associated to finite coverings of $M$. In the case$M=\mathbb{C}^*$, it leads for each positive integer $N$ to a filtration on thespace of tangles in $\mathbb{C}^* \times I$ (or "B-tangles"). We first prove anextension of the Shum--Reshetikhin--Turaev theorem in the framework of braidedmodule category leading to B-tangles invariants. We introduce a category of"$N$-chord diagrams", and use a cyclotomic generalization of Drinfeldassociators, introduced by Enriquez, to put a braided module category structureon it. We show that the corresponding functor from the category of B-tangles isa universal invariant with respect to the $N$ filtration. We show thatVassiliev invariants in the usual sense are well approximated by $N$ finitetype invariants. We show that specializations of the universal invariant can beconstructed from modules over a metrizable Lie algebra equipped with a finiteorder automorphism preserving the metric. In the case the latter is a "Cartan"automorphism, we use a previous work of the author to compute these invariantsexplicitly using quantum groups. Restricted to links, this constructionprovides polynomial invariants.

Cyclotomic associators and finite type invariants for tangles in the solid torus