Related papers: Cohomology of matching rules
In order to look for a well-behaved counterpart to Dolbeault cohomology in D-complex geometry, we study the de Rham cohomology of an almost D-complex manifold and its subgroups made up of the classes admitting invariant, respectively…
Motivated by understanding the limiting case of a certain systolic inequality we study compact Riemannian manifolds having all harmonic 1-forms of constant length. We give complete characterizations as far as K\"ahler and hyperbolic…
Let $A$ be a noetherian ring, $\fa$ an ideal of $A$, and $M$ an $A$--module. Some uniform theorems on the artinianness of certain local cohomology modules are proven in a general situation. They generalize and imply previous results about…
Hodge-filtered derived de Rham cohomology of a ring $R$ can be described (up to completion and shift) as the graded pieces of the even filtration on $\mathrm{HC}^-(R)$. In this paper we show a deformation of this result: If $R$ admits a…
Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten…
Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous…
In this paper, we introduce the concepts of representation and dual representation for averaging Leibniz algebras. We also develop a cohomology theory for these algebras. Additionally, we explore the infinitesimal and formal deformation…
In this expository article, we outline the theory of harmonic differential forms and its consequences. We provide self-contained proofs of the following important results in differential geometry: (1) Hodge theorem, which states that for a…
In this note, (rational) Betti numbers of homotopy colimits for toric diagrams and their classifying spaces are described in terms of sheaf cohomology over CW posets. We prove for any $T$-diagram $D$ over any CW poset that…
We describe the cohomology ring of toric wonderful models for arbitrary building set, including the case of non well-connected ones. Our techniques are based on blowups of posets, on Gr\"obner basis over rings and admissible functions.
We develop a global cohomology theory for number fields by offering topological cohomology groups, an arithmetical duality, a Riemann-Roch type theorem, and two types of vanishing theorem. As applications, we study moduli spaces of…
Let $R$ be a semilocal Dedekind domain. Under certain assumptions, we show that two (not necessarily unimodular) hermitian forms over an $R$-algebra with involution, which are rationally ismorphic and have isomorphic semisimple coradicals,…
Mats Boij and Jonas Soederberg (math.AC/0611081) have conjectured that the Betti table of a Cohen-Macaulay module over a polynomial ring can be decomposed in a certain way as a positive linear combination of Betti tables of modules with…
We study cohomological properties of complex manifolds. In particular, under suitable metric conditions, we extend to higher dimensions a result by A. Teleman, which provides an upper bound for the Bott-Chern cohomology in terms of Betti…
We compute the Cech cohomology with integer coefficients of one-dimensional tiling spaces arising from not just one, but several different substitutions, all acting on the same set of tiles. These calculations involve the introduction of a…
Associative conformal algebras of conformal endomorphisms are of essential importance for the study of finite representations of conformal Lie algebras (Lie vertex algebras). We describe all semisimple algebras of conformal endomorphisms…
We show how certain topological properties of co-K{\"a}hler manifolds derive from those of the K\"ahler manifolds which construct them. We go beyond Betti number results and describe the cohomology algebra structure of co-K\"ahler…
The study of the homology of diagram algebras has emerged as an interesting and important field. In many cases, the homology of a diagram algebra can be identified with the homology of a group. In this paper we have two main aims. Firstly,…
We show that diffraction features of $1D$ quasicrystals can be retrieved from a single topological quantity, the \v{C}ech cohomology group, $\check{H}^{1}\cong\mathbb{Z}^2$, which encodes all relevant combinatorial information of tilings.…
Let A be any finite dimensional Hopf algebra over a field k. We specify the Tate and Tate-Hochschild cohomology for A and introduce cup products that make them become graded rings. We establish the relationship between these rings. In…