Related papers: Logarithmic Hennings invariants for restricted qua…

We reconfigure the Milnor invariant of links in terms of central group extensions and unipotent Magnus embeddings. We also develop a diagrammatic computation of the invariant and compute the first non-vanishing invariants of the Milnor link…

We construct geometrically a universal Jones invariant as a limit of invariants given by graded intersections in configuration spaces. For any fixed level $\mathscr N$, we define a new knot invariant, called ``$\mathscr N^{th}$ Unified…

The HKR (Hennings-Kauffman-Radford) framework is used to construct invariants of 4-thickenings of 2-dimensional CW complexes under 2-deformations (1- and 2- handle slides and creations and cancellations of 1-2 handle pairs). The input of…

We construct non-semisimple $2+1$-TQFTs yielding mapping class group representations in Lyubashenko's spaces. In order to do this, we first generalize Beliakova, Blanchet and Geer's logarithmic Hennings invariants based on quantum…

We consider the ways in which a 4-tangle T inside a unit cube can be extended outside the cube into a knot or link L. We present two links n(T) and d(T) such that the greatest common divisor of the determinants of these two links always…

We define numerical link-homotopy invariants of link maps of any number of components, which naturally generalize the Kirk invariant. The Kirk invariant is a link-homotopy invariant of 2-component link maps given by linking numbers of loops…

We extend the Gordon-Litherland pairing to links in thickened surfaces, and use it to define signature, determinant, and nullity invariants for links that bound (unoriented) spanning surfaces. The invariants are seen to depend only on the…

In this article, we give an elementary construction of homological invariants of links presented by braid closures. The Euler characteristic of this complex is equal to quantum polynomial invariant of link.

This paper generalize [7](math.GT/0601291): We construct new links invariants from g, a type I basic classical Lie superalgebra. The construction uses the existence of an unexpected replacement of the vanishing quantum dimension of typical…

We consider two types of quotients of the integrable modules of $\hat{sl}_2$. These spaces of coinvariants have dimensions described in terms of the Verlinde algebra of level-$k$. We describe monomial bases for the spaces of coinvariants,…

In the first part of this paper, we constructed a filtered U(r)-equivariant stable homotopy type called the spectrum of strict broken symmetries sB(L) of links L given by closing a braid with r strands. We further showed that evaluating…

In this paper we study the tensor powers of the standard representation of the quantum super-algebra $U_q(sl(2|1)$, focusing on the rings of its algebra endomorphisms, called centraliser algebras and denoted by $LG_n$. Their dimensions were…

We give a general fixed parameter tractable algorithm to compute quantum invariants of links presented by diagrams, whose complexity is singly exponential in the carving-width (or the tree-width) of the diagram. In particular, we get a…

An attempt is made to conceptualize the derivation as well as to facilitate the computation of Ohtsuki's rational invariants $\lambda_n$ of integral homology 3-spheres extracted from Reshetikhin-Turaev SU(2) quantum invariants. Several…

We give the fermionic character formulas for the spaces of coinvariants obtained from level $k$ integrable representations of $\hat{\mathfrak sl}_2$. We establish the functional realization of the spaces dual to the coinvariant spaces. We…

Let N_1, N_2, M be smooth manifolds with dim N_1 + dim N_2 +1 = dim M$ and let phi_i, for i=1,2, be smooth mappings of N_i to M with Im phi_1 and Im phi_2 disjoint. The classical linking number lk(phi_1,phi_2) is defined only when…

The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie…

The trace or the $0$th Hochschild--Mitchell homology of a linear category $\mathcal{C}$ may be regarded as a kind of decategorification of $\mathcal{C}$. We compute traces of the two versions $\dot{\mathcal{U}}$ and $\dot{\mathcal{U}}^*$ of…

Three-component links in the 3-dimensional sphere were classified up to link homotopy by John Milnor in his senior thesis, published in 1954. A complete set of invariants is given by the pairwise linking numbers p, q and r of the…

The Reshetikhin-Turaev invariant, Turaev's TQFT, and many related constructions rely on the encoding of certain tangles (n-string links, or ribbon n-handles) as n-forms on the coend of a ribbon category. We introduce the monoidal category…