Results 81 to 90 of about 167,457 (236)

Around the de Rham-Betti conjecture [PDF]

arXiv, 2022
A de Rham-Betti class on a smooth projective variety $X$ over an algebraic extension $K$ of the rational numbers is a rational class in the Betti cohomology of the analytification of$X$ that descends to a class in the algebraic de Rham cohomology of $X$ via the period comparison isomorphism.
arxiv  

Construction of a Finite Element Basis of the First de Rham Cohomology Group and Numerical Solution of 3D Magnetostatic Problems

SIAM Journal on Numerical Analysis, 2013
We devise an efficient algorithm for the finite element approximation of harmonic fields and the numerical solution of three-dimensional magnetostatic problems.
Ana Alonso Rodríguez, E. Bertolazzi, R. Ghiloni, A. Valli   +3 more
semanticscholar   +1 more source

Every finite graph arises as the singular set of a compact 3‐D calibrated area minimizing surface

Communications on Pure and Applied Mathematics, Volume 77, Issue 9, Page 3670-3707, September 2024.
Abstract Given any (not necessarily connected) combinatorial finite graph and any compact smooth 6‐manifold M6$M^6$ with the third Betti number b3≠0$b_3\not=0$, we construct a calibrated 3‐dimensional homologically area minimizing surface on M$M$ equipped in a smooth metric g$g$, so that the singular set of the surface is precisely an embedding of this
Zhenhua Liu
wiley   +1 more source

Knotted families from graspers

Journal of Topology, Volume 17, Issue 2, June 2024.
Abstract For any smooth manifold M$M$ of dimension d⩾4$d\geqslant 4$, we construct explicit classes in homotopy groups of spaces of embeddings of either an arc or a circle into M$M$, in every degree that is a multiple of d−3$d-3$, and show that they are detected in the Taylor tower of Goodwillie and Weiss.
Danica Kosanović
wiley   +1 more source

Quasiregular curves and cohomology

Proceedings of the London Mathematical Society, Volume 128, Issue 5, May 2024.
Abstract Let N$N$ be a closed, connected, and oriented Riemannian manifold, which admits a quasiregular ω$\omega$‐curve Rn→N$\mathbb {R}^n \rightarrow N$ with infinite energy. We prove that, if the de Rham class of ω$\omega$ is nonzero and a finite sum of nontrivial products, then there exists a nontrivial graded algebra homomorphism HdR∗(N)→⋀∗Rn$H_ ...
Susanna Heikkilä
wiley   +1 more source

Cohomologie de de Rham entiere (Integral de Rham cohomology) [PDF]

arXiv, 2004
The Cartier isomorphism allows a nice description of the Bockstein spectral sequence of the de Rham complex over the integers. It is used to compute the integral de Rham cohomology of affine spaces. ----- On decrit la suite spectrale de Bockstein issue du complexe de de Rham sur les entiers.
arxiv  

On q-de Rham cohomology via $$\Lambda $$Λ-rings

Mathematische Annalen, 2016
We show that Aomoto’s q-deformation of de Rham cohomology arises as a natural cohomology theory for $$\Lambda $$Λ-rings. Moreover, Scholze’s $$(q-1)$$(q-1)-adic completion of q-de Rham cohomology depends only on the Adams operations at each residue ...
J. Pridham
semanticscholar   +1 more source

The period isomorphism in the tame geometry

Mathematische Nachrichten, Volume 297, Issue 4, Page 1230-1247, April 2024.
Abstract We describe singular homology of a manifold X$X$ via simplices σ:Δd→X$\sigma :\Delta _d\rightarrow X$ that satisfy Stokes' formula with respect to all differential forms. The notion is geared to the case of the tame geometry (definable manifolds with respect to an o‐minimal structure), where it gives a description of the period pairing with de
Annette Huber
wiley   +1 more source

On the cohomologies of the de Rham complex over weighted isotropic and anisotropic Hölder spaces [PDF]

arXiv, 2021
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 by the de Rham differential $d$ and the operator $d^*$ formally adjoint to it, a description of the cohomology ...
arxiv  

Hilbert complexes with mixed boundary conditions part 3: Biharmonic complexes

Mathematical Methods in the Applied Sciences, Volume 47, Issue 6, Page 3847-3892, April 2024.
We show that the biharmonic Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings that follow by abstract arguments using functional analysis together with particular regular decompositions. Higher Sobolev order results are also proved.
Dirk Pauly, Michael Schomburg
wiley   +1 more source