Related papers: Reduction theorem for lattice cohomology

We propose to study transformations on graphs, and more generally structures, by looking at how the cut-rank (as introduced by Oum) of subsets is affected when going from the input structure to the output structure. We consider…

Let $M$ be a connected, closed, oriented three-manifold and $K$, $L$ two rationally null-homologous oriented simple closed curves in $M$. We give an explicit algorithm for computing the linking number between $K$ and $L$ in terms of a…

We introduce a new class of zero-dimensional weighted complete intersections, by abstracting the essential features of rational cohomology algebras of equal rank homogeneous spaces of compact connected Lie groups. We prove that, on a…

We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an…

The theorem of Barth-Lefschetz is a statement about the cohomology of a submanifold X of some projective space, in a range depending on the codimension of the embedding. Here this is generalized to the case of a submanifold X of a smooth…

The collection of all topologies on the set of three points is studied treating the topology as quantum-like observable. It turns out to be possible under the assumption of the asymmetry between the spaces of bra- and ket-vectors. The…

In two seminal papers M. Kontsevich introduced graph homology as a tool to compute the homology of three infinite dimensional Lie algebras, associated to the three operads `commutative,' `associative' and `Lie.' We generalize his theorem to…

We show that the finiteness length of an $S$-arithmetic subgroup $\Gamma$ in a noncommutative isotropic absolutely almost simple group $G$ over a global function field is one less than the sum of the local ranks of $G$ taken over the places…

We present a scheme for the analytic computation of renormalization functions on the lattice, using a symbolic manipulation computer language. Our first nontrivial application is a new three-loop result for the topological susceptibility.

We investigated SU(3) lattice gauge theory with a fundamental and adjoint plaquette term in the action. The purpose is to test whether the choice of a negative adjoint coupling can reduce lattice artefacts and improve the scaling b…

Given a graph $G$ and a target graph $H$, an $H$-coloring of $G$ is an adjacency-preserving vertex map from $G$ to $H$. The number of $H$-colorings of $G$, $\hom(G,H)$, has been studied for many classes of $G$ and $H$. In particular,…

We study the fixed point subalgebra of a certain class of lattice vertex operator algebras by an automorphism of order 3, which is a lift of a fixed-point-free isometry of the underlying lattice. We classify the irreducible modules for the…

We provide an algorithm for computing an effective basis of homology of elliptic surfaces over the complex projective line on which integration of periods can be carried out. This allows the heuristic recovery of several algebraic…

The symplectic derivation Lie algebras defined by Kontsevich are related to various geometric objects including moduli spaces of graphs and of Riemann surfaces, graph homologies, Hamiltonian vector fields, etc. Each of them and its…

We present a short proof of the following Pontryagin theorem, whose original proof was complicated and has never been published in details: {\bf Theorem.} Let $M$ be a connected oriented closed smooth 3-manifold. Let $L_1(M)$ be the set of…

We propose a new method of computing cohomology groups of spaces of knots in $\R^n$, $n \ge 3$, based on the topology of configuration spaces and two-connected graphs, and calculate all such classes of order $\le 3.$ As a byproduct we…

Lattice reduction smooths the Gram-Schmidt profile, and we use majorization to describe the local swap mechanism behind that smoothing. In this language, each non-degenerate Lov\'asz swap acts as a T-transform on the log-norm profile. As a…

We introduce deformations of lattice cohomology corresponding to the knot homologies found by Ozsv\' ath, Stipsicz and Szab\' o in \cite{OSS4}. By means of holomorphic triangles counting, we prove equivalence with the analytic theory for a…

The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We give characterize multiplicative simple Hom-associative algebras and show some examples deforming the $2\times 2$-matrix algebra…

We construct lattices on six dimensional not completely solvable almost abelian Lie groups, for which the Mostow condition does not hold. For the corresponding compact quotients, we compute the de Rham cohomology (which does not agree in…