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Cohomology and Intersection homology

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Cohomology and Intersection homology

Cohomology vs. Intersection homology

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex. In topology, a branch of mathematics, intersection homology is an analogue of singular homology especially well-suited for the study of singular spaces, discovered by Mark Goresky and Robert MacPherson in the fall of 1974 and developed by them over the next few years.

Similarities between Cohomology and Intersection homology

Cohomology and Intersection homology have 13 things in common (in Unionpedia): Bilinear form, General position, Henri Poincaré, Homology (mathematics), Hyperhomology, Intersection homology, Intersection theory, Manifold, Mathematics, Poincaré duality, Simplicial complex, Singular homology, Topology.

Bilinear form

In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map, where K is the field of scalars.

Bilinear form and Cohomology · Bilinear form and Intersection homology · See more »

General position

In algebraic geometry and computational geometry, general position is a notion of genericity for a set of points, or other geometric objects.

Cohomology and General position · General position and Intersection homology · See more »

Henri Poincaré

Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.

Cohomology and Henri Poincaré · Henri Poincaré and Intersection homology · See more »

Homology (mathematics)

In mathematics, homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.

Cohomology and Homology (mathematics) · Homology (mathematics) and Intersection homology · See more »

Hyperhomology

In homological algebra, the hyperhomology or hypercohomology of a complex of objects of an abelian category is an extension of the usual homology of an object to complexes.

Cohomology and Hyperhomology · Hyperhomology and Intersection homology · See more »

Intersection homology

In topology, a branch of mathematics, intersection homology is an analogue of singular homology especially well-suited for the study of singular spaces, discovered by Mark Goresky and Robert MacPherson in the fall of 1974 and developed by them over the next few years.

Cohomology and Intersection homology · Intersection homology and Intersection homology · See more »

Intersection theory

In mathematics, intersection theory is a branch of algebraic geometry, where subvarieties are intersected on an algebraic variety, and of algebraic topology, where intersections are computed within the cohomology ring.

Cohomology and Intersection theory · Intersection homology and Intersection theory · See more »

Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

Cohomology and Manifold · Intersection homology and Manifold · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

Cohomology and Mathematics · Intersection homology and Mathematics · See more »

Poincaré duality

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.

Cohomology and Poincaré duality · Intersection homology and Poincaré duality · See more »

Simplicial complex

In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration).

Cohomology and Simplicial complex · Intersection homology and Simplicial complex · See more »

Singular homology

In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of algebraic invariants of a topological space X, the so-called homology groups H_n(X).

Cohomology and Singular homology · Intersection homology and Singular homology · See more »

Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

Cohomology and Topology · Intersection homology and Topology · See more »

The list above answers the following questions

Cohomology and Intersection homology Comparison

Cohomology has 186 relations, while Intersection homology has 28. As they have in common 13, the Jaccard index is 6.07% = 13 / (186 + 28).

References

This article shows the relationship between Cohomology and Intersection homology. To access each article from which the information was extracted, please visit:

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