Results 21 to 30 of about 167,457 (236)
The Essence of de Rham Cohomology [PDF]
arXivThe study of differential forms that are closed but not exact reveals important information about the global topology of a manifold, encoded in the de Rham cohomology groups $H^k(M)$, named after Georges de Rham (1903-1990). This expository paper provides an explanation and exploration of de Rham cohomology and its equivalence to singular cohomology ...
arxiv +3 more sources
Divided Powers and Derived De Rham Cohomology [PDF]
arXivWe develop the formalism of derived divided power algebras, and revisit the theory of derived De Rham and derived crystalline cohomology in this framework. We characterize derived De Rham cohomology of a derived commutative algebra $A$ over a base $R$, together with the Hodge filtration on it, in terms of the universal property as the largest filtered ...
Kirill Olegovich Magidson
arxiv +3 more sources
A basis of algebraic de Rham cohomology of complete intersections over a characteristic zero field [PDF]
Communications in Algebra, 2021 Let be a field of characteristic 0. Let X be a smooth complete intersection over of dimension n – k in the projective space for given positive integers n and k.
Jeehoon Park, Junyeong Park
semanticscholar +1 more source
Limiting mixed Hodge structures on the relative log de Rham cohomology groups of a projective semistable log smooth degeneration [PDF]
Kyoto Journal of Mathematics, 2020 We prove that the relative log de Rham cohomology groups of a projective semistable log smooth degeneration admit a natural \textit{limiting} mixed Hodge structure. More precisely, we construct a family of increasing filtrations and a family of nilpotent
T. Fujisawa
semanticscholar +1 more source
A simple construction of the Rumin algebra
Comptes Rendus. Mathématique, 2023 The Rumin algebra of a contact manifold is a contact invariant $C_\infty $-algebra of differential forms which computes the de Rham cohomology algebra.
Case, Jeffrey S.
doaj +1 more source
Bott-Chern hypercohomology and bimeromorphic invariants
Complex Manifolds, 2023 The aim of this article is to study the geometry of Bott-Chern hypercohomology from the bimeromorphic point of view. We construct some new bimeromorphic invariants involving the cohomology for the sheaf of germs of pluriharmonic functions, the truncated ...
Yang Song, Yang Xiangdong
doaj +1 more source
Topological and Geometrical Properties of k-Symplectic Structures
Axioms, 2022 We study new geometrical and topological aspects of polarized k-symplectic manifolds. In addition, we study the De Rham cohomology groups of the k-symplectic group.
Essabab Said +2 more
doaj +1 more source
On Rham cohomology of locally trivial Lie groupoids over triangulated manifolds
Pracì Mìžnarodnogo Geometričnogo Centru, 2020 Based on the isomorphism between Lie algebroid cohomology and piecewise smooth cohomology of a transitive Lie algebroid, 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 ...
Jose R. Oliveira
doaj +1 more source
On the Morse–Novikov Cohomology of blowing up complex manifolds
Comptes Rendus. Mathématique, 2020 Inspired by the recent works of S. Rao–S. Yang–X.-D. Yang and L. Meng on the blow-up formulae for de Rham and Morse–Novikov cohomology groups, we give a new simple proof of the blow-up formula for Morse–Novikov cohomology by introducing the relative ...
Zou, Yongpan
doaj +1 more source
Macaulay matrix for Feynman integrals: linear relations and intersection numbers
Journal of High Energy Physics, 2022 We elaborate on the connection between Gel’fand-Kapranov-Zelevinsky systems, de Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman Integrals.
Vsevolod Chestnov +6 more
doaj +1 more source