Related papers: Superforms, Tropical Cohomology, and Poincar\'e Du…
We give explicit harmonic representatives of Dolbeault cohomology of Oeljeklaus-Toma manifolds and show that they are geometrically Dolbeault formal. We also give explicit harmonic representatives of Bott-Chern cohomology of Oeljeklaus-Toma…
We prove a duality relation for the moduli of the family of curves connecting two sets and the family of surfaces separating the sets, in the setting of a complete metric space equipped with a doubling measure and supporting a Poincar\'e…
The aim of this paper is to study homological properties of tropical fans and to propose a notion of smoothness in tropical geometry, which goes beyond matroids and their Bergman fans and which leads to an enrichment of the category of…
The method of intersection spaces associates cell-complexes depending on a perversity to certain types of stratified pseudomanifolds in such a way that Poincar\'e duality holds between the ordinary rational cohomology groups of the…
We provide base change theorems, projection formulae and Verdier duality for both cohomology and homology in the context of finite topological spaces
We prove a duality for factorization homology which generalizes both usual Poincar\'e duality for manifolds and Koszul duality for $\mathcal{E}_n$-algebras. The duality has application to the Hochschild homology of associative algebras and…
We study the refinement invariance of several intersection (co)homologies existing in the literature. These (co)homologies have been introduced in order to establish the Poincar\'e Duality in variousl contexts. We found the classical…
We construct cup and cap products in intersection (co)homology with field coefficients. The existence of the cap product allows us to give a new proof of Poincare duality in intersection (co)homology which is similar in spirit to the usual…
We prove a conjecture of Bhatt-Hansen that derived pushforwards along proper morphisms of rigid-analytic spaces commute with Verdier duality on Zariski-constructible complexes. In particular, this yields duality statements for the…
We compute bifunctors cohomology for matrix polynomials under conjugation and detect candidates for universal classes in higher invariant theory.
We show that, for a finite spectrum $X$, Spanier-Whitehead duality induces an isomorphism between the cohomological and homological Atiyah-Hirzebruch spectral sequences. As an application, it follows that Poincar\'e duality for a Poincar\'e…
We prove the following version of Poincare duality for reduced $L_{q,p}$-cohomology: For any $1<q,p<\infty$, the $L_{q,p}$-cohomology of a Riemannian manifold is in duality with the interior $L_{p',q'}-cohomology for $1/p+1/p'=1$,…
We give an explicit formula for the duality, previously conjectured by Horja and Borisov, of two systems of GKZ hypergeometric PDEs. We prove that in the appropriate limit this duality can be identified with the inverse of the Euler…
Torsion sensitive intersection homology was introduced to unify several versions of Poincare duality for stratified spaces into a single theorem. This unified duality theorem holds with ground coefficients in an arbitrary PID and with no…
In this article, we pursue the study begun in \cite{Lup02} on the cohomology of rationally elliptic coformal spaces. Consequently, we complete, for such spaces, the proof of Lupton's conjecture and deduce Hilali's.
We study the noncommutative Poincar\'e duality between the Poisson homology and cohomology of unimodular Poisson algebras, and show that Kontsevich's deformation quantization as well as Koszul duality preserve the corresponding Poincar\'e…
We observe that the Poincare duality isomorphism for a string manifold is an isomorphism of modules over the subalgebra A(2) of the modulo 2 Steenrod algebra. In particular, the pattern of the operations Sq^1, Sq^2, and Sq^4 on the…
We dualize previous work on generalized persistence diagrams for filtrations to cofiltrations. When the underlying space is a manifold, we express this duality as a Poincar\'e duality between their generalized persistence diagrams. A heavy…
Tropical manifolds are polyhedral complexes enhanced with certain kind of affine structure. This structure manifests itself through a particular cohomology class which we call the eigenwave of a tropical manifold. Other wave classes of…
Given a compact toric surface, the multiplication of its rational cohomology can be described in terms of the intersection products of Weil divisors, or in terms of the cup products of cohomology classes representing specific cells. In this…