cohomology

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cohomology

(ˌkəʊhəˈmɒlədʒɪ)
n
the abstract study of algebraic topology
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The topics include plateau problems in metric spaces and related homology and cohomology theories, relating equivariant and motivic cohomology via analytic currents, ideal theory and classification on isoparametric hypersurfaces, finite volume flows and Witten's deformation, on the existence and nonexistence of stable submanifolds and currents in positively curved manifolds and the topology of submanifolds in Euclidean spaces, and remarks on stable minimal hypersurfaces in Riemannian manifolds and generalized Bernstein problems.
Bredon, Equivariant Cohomology Theories, Springer-Verlag Lec.
The 16 papers, selected from 35 presentations, include discussions of primitive cycles and the Fourier-Radon transform, the derivative of a normal function associated with a Deligne cohomology class, secondary theories for etale groupiods, finite generation conjectures for motivic cohomology theories over finite fields, and derived categories of coherent sheaves and motives of K3 surfaces.
First published in 2002 as Ippan Kohomoroji, this monograph introduces generalized cohomology theories to mathematical audiences who are not necessarily experts in algebraic topology.
In this situation each of the corresponding cohomology theories gives rise to a formal group law, and the interaction of these two laws forms a central pillar of their theory.
The nine papers discuss an enlarged version of Morita equivalence, moduli spaces of commutative ring spectra, cohomology theories for highly structured ring spectra, higher coherences in equivariant K-theory, and permutative categories as a model of connective stable homotopy.
Ravenel studied complex oriented cohomology theories for the classifying space BG and succeeded, as a generalisation of Atiyah's theorem cited above, in constructing generalized group characters which describe certain periodic cohomologies of BG (modulo torsion elements which conjecturally do not exist) [12] (see also [13, 11, 16]).