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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.
In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds. It states that if M is an n -dimensional oriented closed manifold ( compact and without boundary), then the k th cohomology group of M is isomorphic to the ( n − k ) th ...
2. Nov. 2021 · One of the most important properties of intersection homology is the generalization of the Poincaré-Lefschetz duality, i.e. the intersection pairing (Sect. 5.2.6).
- Jean-Paul Brasselet
- jean-paul.brasselet@univ-amu.fr
The fundamental propositions of the Poincare-Lefschetz intersection theory hold for the intersection homology groups of a pseudomanifold X in the following sense: (1) (82.1) Suppose jj + (r I 7 are perversities and suppose V is a cycle for IH? (X) and W is a cycle for ZHp(X).
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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.
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
4. Apr. 2008 · In this paper, we give an algebraic formulation that extends persistence to essential homology for any filtered space, present an algorithm to calculate it, and describe how it aids our ability to recognize shape features for codimension 1 submanifolds of Euclidean space.
