Information om | Engelska ordet COHOMOLOGICAL

Exempel på hur man kan använda COHOMOLOGICAL i en mening

• Together with his advisor Emil Artin, Tate gave a cohomological treatment of global class field theory using techniques of group cohomology applied to the idele class group and Galois cohomology.
• Pierre Deligne calls the supersymmetric one the super gradation, and the classical one the cohomological gradation.
• In particular, they solve the anisotropic Plateau problem in arbitrary dimension and codimension for any collection of rectifiable sets satisfying a combination of general homological, cohomological or homotopical spanning conditions.
• Later, with the rise of cohomology theory in the 1930s, he contributed to the intersection number approach (that is, in cohomological terms, the ring structure) via the cup product and duality on manifolds.
• The cohomological Brauer group of a quasi-compact scheme X is defined to be the torsion subgroup of the étale cohomology group.
• More generally, the fundamental group of a closed, connected, orientable aspherical manifold of dimension n has cohomological dimension n.
• Applied to data, those cohomological tools quantifies statistical dependences and independences, including Markov chains and conditional independence, in the multivariate case.
• His long term collaboration with Maxim Kontsevich is devoted to various aspects of homological mirror symmetry, a proof of Deligne conjecture about operations on the cohomological Hochschild complex, a direct construction of Calabi-Yau varieties based on SYZ conjecture and non-archimedean geometry, and more recently to Donaldson-Thomas theory.
• The Witten conjecture is a special case of a more general relation between integrable systems of Hamiltonian PDEs and the geometry of certain families of 2D topological field theories (axiomatized in the form of the so-called cohomological field theories by Kontsevich and Manin), which was explored and studied systematically by B.
• As for Kähler metrics, the above definition of a balanced metric automatically places cohomological restrictions on the underlying manifold; by Stokes' theorem, every codimension-one complex subvariety is homologically nontrivial.
• Having become familiar with the work of Spencer, Goldschmidt and Quillen on formal integrability, he turned his attention to the algebraic (in particular, cohomological) component of that theory.

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