Suchergebnisse
Suchergebnisse:
In mathematics, Lefschetz duality is a version of Poincaré duality in geometric topology, applying to a manifold with boundary. Such a formulation was introduced by Solomon Lefschetz , at the same time introducing relative homology, for application to the Lefschetz fixed-point theorem.
The Poincaré–Lefschetz duality theorem is a generalisation for manifolds with boundary. In the non-orientable case, taking into account the sheaf of local orientations, one can give a statement that is independent of orientability: see twisted Poincaré duality .
4. Dez. 2019 · The Poincare-Alexander-Lefschetz duality. Ask Question. Asked 4 years, 4 months ago. Modified 4 years, 3 months ago. Viewed 2k times. 6. I came across the Poincare-Alexander-Lefschetz duality here: If M M is a closed (compact and no boundary) manifold, B ⊂ A ⊂ M B ⊂ A ⊂ M are closed subsets, then.
2. Nov. 2021 · Lefschetz duality for intersection (co)homology. Article24 May 2018. 5.1 Introduction. In the case of manifolds, global homological invariants like Betti numbers enjoy remarkable duality properties as stated by Poincaré (1893) and Lefschetz (1926).
- Jean-Paul Brasselet
- jean-paul.brasselet@univ-amu.fr
7. März 2022 · Poincaré–Lefschetz duality can easily be applied to describe a duality between the homology and the cohomology of a manifold with boundary.
27. Sept. 2020 · The cohomology rings of smooth complex projective algebraic varieties satisfy a “package” of properties: Poincaré duality, weak Lefschetz, hard Lefschetz, and the Hodge–Riemann bilinear relations. These properties impose conditions on the structure of the cohomology ring, and give rise to interesting linear operators and ...
17. Apr. 2023 · Lefschetz–Poincaré duality. An assertion about the duality between homology and cohomology, established by S. Lefschetz. More precisely, if $(X,A)$ is a pair of spaces such that $X\setminus A$ is an $n$-dimensional topological manifold, then for any Abelian group $G$ and any $i$ there is an isomorphism
