Related papers: An odd Khovanov homotopy type

In this paper, we discuss two topics: first, we show how to convert 1+1-topological quantum field theories valued in symmetric bimonoidal categories into stable homotopical data, using a machinery by Elmendorf and Mandell. Then, we discuss,…

We define Khovanov homology mod 2 for graph-links.

We show that the reduced sl(n) homology defined by Khovanov and Rozansky is invariant under component-preserving positive mutation when n is odd.

We discuss links in thickened surfaces. We define the Khovanov-Lipshitz-Sarkar stable homotopy type and the Steenrod square for the homotopical Khovanov homology of links in thickened surfaces with genus$>1$. A surface means a closed…

We discuss the homotopy type and the cohomology of spaces of locally convex parametrized curves gamma: [0,1] -> S^2, i.e., curves with positive geodesic curvature. The space of all such curves with gamma(0) = gamma(1) = e_1 and gamma'(0) =…

The purpose of this paper is to construct and study equivariant Khovanov homology - a version of Khovanov homology theory for periodic links. Since our construction works regardless of the characteristic of the coefficient ring it…

We study a module structure on Khovanov homology, which we show is natural under the Ozsvath-Szabo spectral sequence to the Floer homology of the branched double cover. As an application, we show that this module structure detects trivial…

We use K-area homology to summarize some results about the Novikov conjecture and the Hirzebruch L-class. In fact, we provide necessary and sufficient conditions for closed manifolds to have a homotopy invariant L-class. In order to obtain…

In [Rie08], the second author defined a Landau-Ginzburg model for homogeneous spaces G/P. In this paper, we reformulate this LG model in the case of the odd-dimensional quadric X=Q_{2m-1}. Namely we introduce a regular function Wcan on a…

We establish a homotopy-theoretic description of the homology of stable moduli spaces of $(2n+1)$-dimensional manifold triads $(N, \partial^h N, \partial^v N)$ with fixed $\partial^v N$, whenever $n \geq 3$ and $(N, \partial^h N)$ is…

We construct an endomorphism of the Khovanov invariant to prove H-thinness and pairing phenomena of the invariants for alternating links. As a consequence, it follows that the Khovanov invariant of an oriented nonsplit alternating link is…

Let X and Y be finite-type CW-complexes (X connected, Y simply connected), such that the rational cohomology ring of Y is a k-rescaling of the rational cohomology ring of X. Assume H^*(X,Q) is a Koszul algebra. Then, the homotopy Lie…

We prove that the Khovanov homology of alternating knots and 2-component links is equal (as a singly graded group) to the singular homology of a certain space of trace- free, binary dihedral representations of the link group. More…

Given a link in the thickened annulus, its annular Khovanov homology carries an action of the Lie algebra $\mathfrak{sl}_2$, which is natural with respect to annular link cobordisms. We consider the problem of lifting this action to the…

We prove that the factorization homologies of a scheme with coefficients in truncated polynomial algebras compute the cohomologies of its generalized configuration spaces. Using Koszul duality between commutative algebras and Lie algebras,…

We develop a space-level formulation of Khovanov skein homology by constructing a stable homotopy type for annular links. We explicitly define a cover functor from the skein flow category to the cube flow category, thereby establishing the…

Let $B$ denote the upper triangular subgroup of $SL_2(C)$, $T$ its diagonal torus and $U$ its unipotent radical. A complex projective variety $Y$ endowed with an algebraic action of $B$ such that the fixed point set $Y^U$ is a single point,…

Given a knot, we ask how its Khovanov and Khovanov-Rozansky homologies change under the operation of introducing twists in a pair of strands. We obtain long exact sequences in homology and further algebraic structure which is then used to…

In this paper, we study the Khovanov homology of an alternating virtual link $L$ and show that it is supported on $g+2$ diagonal lines, where $g$ equals the virtual genus of $L$. Specifically, we show that $Kh^{i,j}(L)$ is supported on the…

We show that the reduced Khovanov homology of an oriented link $L$ in $S^3$ can be expressed as the homology of a chain complex constructed from a description of $L$ as the closure of a 1-tangle diagram $T$ in the annulus. Our chain complex…