Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. A theory associating a system of quotient groups to each topological space.
  • n. A system of quotient groups associated to a topological space.

Etymologies

From co- + homology (Wiktionary)

Examples

  • Section 33.9 is six pages of Penrose trying to explain "sheaf cohomology" whose ideas "… are fairly sophisticated mathematically, but actually very natural."

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  • Section 33.10 explains how positive/negative frequency splitting along with "holomorphic first sheaf cohomology" plays "a direct role in generating deformations of twistor space."

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  • This then leads us into some very rich theory of the algebraic topology of the Dirac operator and something called quantum cohomology.

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  • BRST then becomes essentially Lie algebra cohomology, where you construct the invariant, trivial piece of a representation by cancelling a sequence of non-trivial representations against each other.

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  • The action of a real semisimple lie group on a complex flag manifold, II: Unitary representations on partially holomorphic cohomology spaces by Joseph Albert Wolf

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  • On the mixed Hodge structure on the cohomology of the Milnor fibre.

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  • Several mathematical concepts have been named after him including the Tate module, Tate curve, Tate cycle, Hodge-Tate decompositions, Tate cohomology, Serre-Tate parameter, and Lubin-Tate group.

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  • Several mathematical concepts have been named after him, including the Tate module, Tate curve, Tate cycle, Hodge-Tate decompositions, Tate cohomology, Serre-Tate parameter and

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  • This gives rise to a slogan "when you have partitions of unity, sheaf cohomology vanishes."

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  • So any theorem about sheaf cohomology vanishing on affine spaces needs to be phrased carefully.

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