Related papers: A computer algorithm for the BGG resolution
Sheaf cohomology or, more generally, higher direct images of coherent sheaves along proper morphisms are central to modern algebraic geometry. However, the computation of these objects is a non-trivial and expensive task which easily…
Cohomology operations (including the cohomology ring) of a geometric object are finer algebraic invariants than the homology of it. In the literature, there exist various algorithms for computing the homology groups of simplicial complexes…
In this article we refer to "the BGG method" as a method in which by using Lie-algebra techniques one produces a complex of coherent sheaves on a Shimura variety, which is quasi-isomorphic to the de Rham complex of an automorphic vector…
We introduce the partition function of edge-colored graph homomorphisms, of which the usual partition function of graph homomorphisms is a specialization, and present an efficient algorithm to approximate it in a certain domain. Corollaries…
This thesis deals with the algorithmic representation of constructible sheaves of abelian groups on the \'etale site of a variety over an algebraically closed field, as well as the explicit computation of their cohomology. We describe three…
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
In a previous paper (q-alg/9501022) we suggested some algorithms that could be useful in solving the problem of knot classification. Here we continue this discussion by answering questions raised in that paper and by commenting on practical…
Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology. We develop an algorithm for simplifying the computation of cellular sheaf cohomology via (discrete) Morse-theoretic…
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here "compute" means to find a presentation in terms of generators and relations, and involves only the…
Higher order cohomology of arithmetic groups is expressed in terms of (g,K)-cohomology. Generalizing results of Borel, it is shown that the latter can be computed using functions of (uniform) moderate growth. A higher order versions of…
We give several algorithms addressing computations of intersections of conjugate subgroups.
We present an overview of computational methods for Bredon cohomology with a special focus on infinite groups
Genetic Programming (GP) has found various applications. Understanding this type of algorithm from a theoretical point of view is a challenging task. The first results on the computational complexity of GP have been obtained for problems…
Computations in the cohomology of finite groups.
Determining visibility in planar polygons and arrangements is an important subroutine for many algorithms in computational geometry. In this paper, we report on new implementations, and corresponding experimental evaluations, for two…
This paper deals with computing topological invariants such as connected components, boundary surface genus, and homology groups. For each input data set, we have designed or implemented algorithms to calculate connected components,…
We give an algorithm to compute the following cohomology groups on $U = \C^n \setminus V(f)$ for any non-zero polynomial $f \in \Q[x_1, ..., x_n]$; 1. $H^k(U, \C_U)$, $\C_U$ is the constant sheaf on $U$ with stalk $\C$. 2. $H^k(U, \Vsc)$,…
We show how to induce products in sheaf cohomology for a wide variety of coefficients: sheaves of dg commutative and Lie algebras, symmetric Omega-spectra, filtered dg algebras, operads and operad algebras.
Using the Kontsevich's moduli space of stable maps, we define the equivariant quantum cohomology for generalized flag varieties and make a rigorous computation of quantum cohomology of flag varieties.
In this review, novel non-standard techniques for the computation of cohomology classes on toric varieties are summarized. After an introduction of the basic definitions and properties of toric geometry, we discuss a specific computational…