cohomology group

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cohomology group

[′kō·hə′mäl·ə·jē ‚grüp]
(mathematics)
One of a series of Abelian groups Hn (K) that are used in the study of a simplicial complex K and are closely related to homology groups, being associated with cocycles and coboundaries in the same manner as homology groups are associated with cycles and boundaries.
References in periodicals archive ?
We deal with the following specific topics: vanishing cohomology of isolated and non-isolated singularities.
Jacob Lurie , Harvard University, for his work on the foundations of higher category theory and derived algebraic geometry; for the classification of fully extended topological quantum field theories; and for providing a moduli-theoretic interpretation of elliptic cohomology.
The preliminary chapters discuss singularity theory for KAM tori, review methodology and present a flow chart of the monograph, and present notation, geometric and analytic background, symplectic deformations, and cohomology equations.
Hotta-Springer [11] and Garsia-Procesi [9] discovered that the cohomology ring of the Springer fiber indexed by a partition p of n is isomorphic to certain quotient ring of F[X], which admits a graded [G.
Borel, Cohomology des espaces localement compacts d'apres J.
Provided these are not elements of the first cohomology class and, by the Poincare lemma, they must be locally exact, that is, [e.
Among the topics are upper bounds for the Whitehead-length of mapping spaces, the rational homotopy of symmetric products and spaces of finite subsets, the triviality of adjount bundles, spaces of algebraic maps from real projective spaces into complex projective spaces, the rational cohomology of the total space of the universal fibration with an elliptic fibre, and the localization of group-like function and section spaces with compact domain.
17] Liliana Maxim-Raileanu: Cohomology of Lie algebroids, An.
His sophisticated mathematical investigation evaluated ways to associate algebraic structures to topological spaces and proved that loop homology and Hochschild cohomology coincide for an important class of spaces.
Vaintrob proved that loop homology and Hochschild cohomology coincide for an important class of spaces.