arXiv research

The paper finds Chern-Simons forms for specific classes in simplicial de Rham complex.

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

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

We exhibit a cocycle in the simplicial de Rham complex which represents the Euler class. As an application, we construct a Lie algebra cocycle on $L\mathfrak{so}(4)$.

On the basis of A. L. Carey, D. Crowley, M. K. Murray's work, we exhibit a cocycle in the simplicial de Rham complex which represents the Dixmier-Douady class.

On the basis of Dupont's work, we exhibit a cocycle in the simplicial de Rham complex which represents the Chern character. We also prove the related conjecture due to Brylinski. This gives a way to construct a cocycle in a local truncated complex.

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

De Rham theorem extended to Orlicz cohomology.

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

New cochain algebra for diffeological spaces connects de Rham and singular cohomologies.

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…

When a Lie group $G$ has a central $U(1)$-extension, there is a cocycle in the simplicial de Rham complex $Ω^3(NG)$ which represents the Dixmier-Douady class. Mickelsson and Brylinski, McLaughlin constructed a central $U(1)$-extension $\widehat{LSU(2)} \rightarrow LSU(2)$ whose Dixmier-Douady class in $Ω^3(NLSU(2))$ is…

A C-infinity ring is a set equipped with n-ary operations corresponding to smooth n-ary functions on the real line (satisfying natural axioms). We prove that the cosimplicial abelian group associated to the de Rham complex of Euclidean space has the structure of a cosimplicial C-infinity ring. We also analyse the notio…

We prove that Chern-Weil forms are the only natural differential forms associated to a connection on a principal G-bundle. We use the homotopy theory of simplicial sheaves on smooth manifolds to formulate the theorem and set up the proof. Other arguments come from classical invariant theory. We identify the Weil algebr…

Rust library solves complex equations on abstract simplicial complexes.

Let G be a general (not necessarily finite dimensional compact) Lie group, let g be its Lie algebra, let Cg be the cone on g in the category of differential graded Lie algebras, and consider the functor which assigns to a chain complex V the V-valued total de Rham complex of G. We describe the G-equivariant de Rham coh…

Rham cohomology of Lie groupoids over triangulated manifolds is isomorphic to piecewise cohomology.

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…

Study describes global sections of chiral de Rham complex on compact Ricci-flat Kähler manifolds.

Study calculates global sections on complex curves.

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

In this paper we propose a new treatment about infinite dimensional manifolds, using the language of category and functor. Our definition of infinite dimensional manifolds is a natural generalization of finite dimensional manifolds in the sense that de Rham cohomology and singular cohomology can be naturally defined an…

We define analytic torsion for the twisted de Rham complex, consisting of the spaces of differential forms on a compact oriented Riemannian manifold X valued in a flat vector bundle E, with a differential given by a flat connection on E plus an odd-degree closed differential form H on X. The difficulty lies in the fact…

Positive simplicial volume found for certain non-positively curved manifolds with specific submanifolds.

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

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…

Formula derived for cohomology of local systems on complex manifolds.

Local index density of perturbed de Rham complex is invariant under certain conditions.

We describe an $A_\infty$-quasi-equivalence of dg-categories between the first authors' $\mathcal{P}_{\mathcal{A}}$ ---the category of category of prefect $A^0$-modules with flat $\Z$-connection, corresponding to the de Rham dga $\mathcal{A}$ of a compact manifold $M$--- and the dg-category of \emph{infinity-local syst…

New $A_\infty$ structures derived from equivariant de Rham complex for $S^1$-action.

Introduces a framework for rational homotopy theory in diffeological spaces.

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

Study calculates global sections on special geometric spaces.

Develops combinatorial theory of vector bundles on simplicial complexes.

We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover X' \to X. The completion of this complex in exponentially weighted L^2-norms is Fredholm for all but finitely many exceptional weights determined by the eigenvalues of the covering translation map H_*(X') \to H_*(X…

In this paper, we extend the Burghelea-Haller analytic torsion to the twisted de Rham complexes. We also compare it with the twisted refined analytic torsion defined by Huang.

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

Locally-verifiable conditions ensure exactness of spline discrete de Rham complex.

We introduce the notion of a conformal de Rham complex of a Riemannian manifold. This is a graded differential Banach algebra and it is invariant under quasiconformal maps, in particular the associated cohomology is a new quasiconformal invariant.

We characterize Lie group actions for which there exists, at least locally, an evaluation map that defines a cochain map from the differential complex of invariant forms on a manifold to the De Rham complex for the quotient.

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

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

We show that the chiral de Rham complex of a generalized Calabi-Yau manifold carries N=2 supersymmetry. We discuss the corresponding topological twist for this N=2 algebra. We interpret this as an algebroid version of the super-Sugawara or Kac-Todorov construction.

Develops fractional de Rham theory for Maxwell equations.

A classical result in differential geometry states that for a free and proper Lie group action, the quotient map to the orbit space induces an isomorphism between the de Rham complex of differential forms on the orbit space and the basic differential forms on the original manifold. In this paper, this result is general…

Constructs a universal Chern-Weil map for infinite dimensional Lie groups.

Simplicial versions of topological abelian gauge theories are constructed which reproduce the continuum expressions for the partition function and Wilson expectation value of linked loops, expressible in terms of R-torsion and linking numbers respectively. The new feature which makes this possible is the introduction o…

Study shows gap between de Rham and symplectic-Bott-Chern harmonic forms for specific almost-Kähler manifolds.