arXiv research

Introduces a framework for rational homotopy theory in diffeological spaces.

De Rham theorem extended to Orlicz cohomology.

Study of de Rham cohomology on non-Hausdorff manifolds.

Two de Rham complexes in diffeology are compared using a factor map.

Investigates Künneth formula for foliated de Rham cohomology, overcoming non-Hausdorff issues.

Study de Rham homomorphism for Lipschitz cohomologies on metric simplicial complexes.

New Lipschitz de Rham theorem for $L_p$-cohomology.

Authors prove de Rham cohomology of Poisson and Jacobi manifolds is trivial.

Based in the isomorphism between Lie algebroid cohomology and piecewise smooth cohomology, it is proved that the Rham cohomology of a locally trivial Lie groupoid $G$ on a smooth manifold $M$ is isomorphic to the piecewise Rham cohomology of $G$, in which $G$ and $M$ are manifolds without boundary and $M$ is smoothly t…

We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.

Researchers compute de Rham cohomology of geodesic flow foliations on hyperbolic surfaces.

Study new invariants in complex geometry using Bott-Chern hypercohomology.

New cohomology theory for diffeological spaces developed.

The paper explores de Rham theory for singular spaces and stacks.

We define quantum exterior product wedge_h and quantum exterior differential d_h on Poisson manifolds (of which symplectic manifolds are an important class of examples). Quantum de Rham cohomology, which is a deformation quantization of de Rham cohomology, is defined as the cohomology of d_h. We also define quantum Dol…

This paper extends de Rham theory of smooth manifolds to exploded manifolds. Included are versions of Stokes' theorem, De Rham cohomology, Poincare duality, and integration along the fiber. The resulting cohomology theory is used to define Gromov Witten invariants of exploded manifolds in a separate paper.

Given a compact stratified pseudomanifold with a Thom-Mather stratification and a class of riemannian metrics over its regular part, we study the relationships between the $L^{2}$ de Rham and Hodge cohomology and the intersection cohomology of $X$ associated to some perversities. More precisely, to a kind of metric whi…

Extended Regge complex for linearized Riemann-Cartan geometry and cohomology.

Using the language and terminology of relative homological algebra, in particular that of derived functors, we introduce equivariant cohomology over a general Lie-Rinehart algebra and equivariant de Rham cohomology over a locally trivial Lie groupoid in terms of suitably defined monads (also known as triples) and the a…

The purpose of this paper is to present a ``Cech-De Rham'' model for the cohomology of leaf spaces. This model lends itself to the construction of characteristic classes (in the cohomology of classifying spaces) by explicit geometrical constructions which are immediate extensions of the standard constructions for manif…

We define quantum exterior product wedge_h and quantum exterior differential d_h on Poisson manifolds, of which symplectic manifolds are an important class of examples. Quantum de Rham cohomology is defined as the cohomology of d_h. We also define quantum Dolbeault cohomology. Quantum hard Lefschetz theorem is proved. …

The primitive cohomology of Calabi-Yau intersections is described using a twisted de Rham complex.

This is a survey on the equivariant cohomology of Lie group actions on manifolds, from the point of view of de Rham theory. Emphasis is put on the notion of equivariant formality, as well as on applications to ordinary cohomology and to fixed points.

We derive a blow-up formula for the de Rham cohomology of a local system of complex vector spaces on a compact complex manifold. As an application, we obtain the blow-up invariance of $E_{1}$-degeneracy of the Hodge-de Rham spectral sequence associated to a local system of complex vector spaces.

The Burde--de Rham theorem is extended to finitely presented pro-$p$ groups with specific conditions.

We prove an analogue of the de Rham theorem for the extended L^2-cohomology introduced by M. Farber. This is done by establishing that the de Rham complex over a compact closed manifold with coefficients in a flat Hilbert bundle E of A-modules over a finite von Neumann algebra A is chain-homotopy equivalent (with bound…

We identify two Frobenius manifolds obtained from two different differential Gerstenhaber-Batalin-Vilkovisky algebras on a compact Kaehler manifold. One is constructed on the Dolbeault cohomology, and the other on the de Rham cohomology. Our result can be considered as a generalization of the identification of the Dolb…

Study mapping class group action on de Rham quasimorphisms, finding no fixed points.

Study cohomology of odd symplectic manifolds, linking to Lagrangian submanifolds and BV Laplacians.

Cohomology of Lie group quotient equals Lie algebra cohomology.

We endow the de Rham cohomology of any Poisson or Jacobi manifold with a natural homotopy Frobenius manifold structure. This result relies on a minimal model theorem for multicomplexes and a new kind of a Hodge degeneration condition.

We show that the de Rham theorem, interpreted as the isomorphism between distributional de Rham cohomology and simplicial homology in the dual dimension for a simplicial decomposition of a compact oriented manifold, is a straightforward consequence of elementary properties of currents. The explicit construction of this…

Generalizes integration map to coinvariants of bounded functions.

Proves cup product homomorphism for bounded cohomology on negatively curved manifolds.

The article examines twisted cohomologies on algebraic and analytic varieties.

The paper studies twisted Morse homology and cohomology on manifolds.

Graph theory connects automorphisms to cohomology.

Explains Hodge theory and Kodaira embedding theorem for complex manifolds.

Study reveals a link between Ruelle-Pollicott resonances and cohomology eigenvalues for Anosov diffeomorphisms.

Study on Čech-de Rham obstruction in diffeological spaces.

Study Hodge-de Rham numbers for almost complex 4-manifolds, extending properties from complex surfaces.

We use Hodge theory and a construction of Merkulov to construct $A_{\infty}$ structures on de Rham cohomology and Dolbeault cohomology.

New cohomology groups generalize Euler number for Lie superalgebras.

New classification for certain 4-manifolds using quasiregular mappings.

For a simply connected (non-nilpotent) solvable Lie group $G$ with a lattice $Γ$ the de Rham and Dolbeault cohomologies of the solvmanifold $G/Γ$ are not in general isomorphic to the cohomologies of the Lie algebra $\mathfrak g$ of $G$. In this paper we construct, up to a finite group, a new Lie algebra $\tilde{\mathfr…

We prove transverse Weitzenböck identities for the horizontal Laplacians of a totally geodesic foliation. As a consequence, we obtain nullity theorems for the de Rham cohomology assuming only the positivity of curvature quantities transverse to the leaves. Those curvature quantities appear in the adiabatic limit of the…

Degree one twisting of Deligne cohomology, as a differential refinement of integral cohomology, was established in previous work. Here we consider higher degree twists. The Rham complex, hence de Rham cohomology, admits twists of any odd degree. However, in order to consider twists of integral cohomology we need a peri…

The chiral de Rham complex of Malikov, Schechtman, and Vaintrob, is a sheaf of differential graded vertex algebras that exists on any smooth manifold $Z$, and contains the ordinary de Rham complex at weight zero. Given a closed 3-form $H$ on $Z$, we construct the twisted chiral de Rham differential $D_H$, which coincid…