Related papers: Computing Adem Cohomology Operations
We study connected sum at infinity on smooth, open manifolds. This operation requires a choice of proper ray in each manifold summand. In favorable circumstances, the connected sum at infinity operation is independent of ray choices. For…
We describe algorithms for finding harmonic cochains, an essential ingredient for solving elliptic partial differential equations in exterior calculus. Harmonic cochains are also useful in computational topology and computer graphics. We…
We introduce the notion of compatible actions in the context of split extensions of finite dimensional Lie algebras over a field. Using compatible actions, we construct a new resolution to compute the cohomology of semi-direct products of…
The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences. In this paper we discuss the problem of discretizing vector-valued functions…
Cohomology of the variational bicomplex in the calculus of variations in classical field theory are computed in the class of exteriror forms of finite jet order. This provides a solution of the global inverse problem of the finite order…
An abelian arrangement is a finite set of codimension one abelian subvarieties (possibly translated) in a complex abelian variety. In this paper, we study the cohomology of the complement of an abelian arrangement. For unimodular abelian…
We introduce Deligne cohomology that classifies U(1) fibre bundles over 3-manifolds endowed with connections. We show how the structure of Deligne cohomology classes provides a way to perform exact (non-perturbative) computations in U(1)…
This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with corners. Special attention is given to the pull-back product…
Let $k$ be a perfect field of characteristic $p > 0$, $W_n = W_n(k)$. For separated $k$-schemes of finite type, we explain how rigid cohomology with compact supports can be computed as the cohomology of certain de Rham-Witt complexes with…
We compute the Betti numbers and describe the cohomology algebras of the ordered and unordered configuration spaces of three points in complex projective spaces, including the infinite dimensional case. We also compute these invariants for…
Adams operations are the natural transformations of the representation ring functor on the category of finite groups, and they are one way to describe the usual lambda-ring structure on these rings. From the representation-theoretical point…
In this paper we construct an analog of Steenrod operations in motivic cohomology and prove their basic properties including the Cartan formula, the Adem relations and the realtions to characteristic classes.
Developing ideas of \cite{Fei}, we introduce canonical cosimplicial cohomology of meromorphic functions for infinite-dimensional Lie algebra formal series with prescribed analytic behavior on domains of a complex manifold $M$. Graded…
We define a monoid structure on the set of $k$-equal arrangements and use this structure to define limits of braid arrangements. We compute the cohomology of the associated limits of rational models of the arrangements complex complements.…
This paper presents some algorithmic techniques to compute explicitly the noetherian operators associated to a class of ideals and modules over a polynomial ring. The procedures we include in this work can be easily encoded in computer…
We derive a cohomological formula for the analytic index of the Dirac-Ramond operator and we exhibit its modular properties.
We consider the de Rham complex over scales of weighted isotropic and anisotropic H\"older spaces with prescribed asymptotic behaviour at the infinity. Starting from theorems on the solvability of the system of operator equations generated…
Complexity one spaces are an important class of examples in symplectic geometry. Karshon and Tolman classify them in terms of combinatorial and topological data. In this paper, we compute the equivariant cohomology for any complexity one…
It is known that the computation of the Poisson cohomology is closely related to the classification of singularities of Poisson structures. In this paper, we will first look for the normal forms of germs at (0,0) of Poisson structures on…
We calculate the rational cohomology of the classifying space of the diffeomorphism group of the manifolds $U_{g,1}^n:= \#^g(S^n \times S^{n+1})\setminus \mathrm{int}{D^{2n+1}}$, for large $g$ and $n$, up to approximately degree $n$. The…