相关论文: Categorified Jones-Wenzl Projectors: a comparison

We introduce the notion of a categorical join, which can be thought of as a categorification of the classical join of two projective varieties. This notion is in the spirit of homological projective duality, which categorifies classical…

We propose a means by which some categorifications can be evaluated at a root of unity. This is implemented using a suitable localization in the context of prior work by the authors on categorification of the Jones-Wenzl projectors. Within…

An important goal in studying the relations between unitary VOAs and conformal nets is to prove the equivalence of their ribbon categories. In this article, we prove this conjecture for many familiar examples. Our main idea is to construct…

In \cite{LS14} the analogy between the Kleisli construction and the construction of "warping a skew monoidale category" in the sense of \cite{LS12} was outlined. In this note we present the same work in a slightly more formal way.

Based on different views on the Jones polynomial we review representation theoretic categorified link and tangle invariants. We unify them in a common combinatorial framework and connect them via the theory of Soergel bimodules. The…

This is a short survey of algebro-combinatorial link homology theories which have the Jones polynomial and other link polynomials as their Euler characteristics.

Trivalent plane graphs are used in various areas of mathematics which relate for instance to the colored Jones polynomial, invariants of 3-manifolds and quantum computation. Their evaluation is based on computations in the Temperley-Lieb…

We describe algebraically, diagrammatically and in terms of weight vectors, the restriction of tensor powers of the standard representation of quantum $\mathfrak{sl}_2$ to a coideal subalgebra. We realise the category as module category…

As put forward in [arXiv:1907.12339] topological quantum field theories can be projected using so-called projection defects. The projected theory and its correlation functions can be completely realized within the unprojected one. An…

We discuss a new perspective on Khovanov homology, using categorifications of tensor products. While in many ways more technically demanding than Khovanov's approach (and its extension by Bar-Natan), this has distinct advantage of directly…

We construct and study a lift of Jones-Wenzl projectors to the setting of Khovanov spectra, and provide a realization of such lifted projectors via a Cooper-Krushkal-like sequence of maps. We also give a polynomial action on the 3-strand…

Toric subvarieties of projective space are classified up to projective automorphisms.

We investigate several categories related to transition structures, using a mixture of algebraic and topological methods. We show how two such categories are connected by a contravariant adjunction. This is the most detailed of a family of…

We construct a categorification of the quantum sl_3 projectors, the sl_3 analog of the Jones-Wenzl projectors, as the stable limit of the complexes assigned to k-twist torus braids (as k goes to infinity) in a suitably shifted version of…

We present projective versions of the center point theorem and Tverberg's theorem, interpolating between the original and the so-called "dual" center point and Tverberg theorems. Furthermore we give a common generalization of these and many…

We give a diagrammatic presentation for the category of Soergel bimodules for the dihedral group W . The (two-colored) Temperley-Lieb category is embedded inside this category as the degree 0 morphisms between color-alternating objects. The…

We construct a bigraded cohomology theory of links whose Euler characteristic is the Jones polynomial.

Given a stratified topological space, we answer the question whether the functor from the derived category of constructible sheaves to the derived category of sheaves with constructible cohomology is an equivalence. We also establish basic…

We introduce a theory of multigraded Cayley-Chow forms associated to subvarieties of products of projective spaces. Two new phenomena arise: first, the construction turns out to require certain inequalities on the dimensions of projections;…

This paper aims to answer the following question: Given an adjunction between two categories, how is Quillen (co)homology in one category related to that in the other? We identify the induced comparison diagram, giving necessary and…