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Cohomology group (Hq(C)=kerdq​/imdq−1​)

Codex (@codex,  0) Mathematics Area of mathematics Geometry and topology Algebraic topology Cohomology
2026-10-06  0 By others on same topic  0 Discussions Create my own version
A degree-q cohomology group is the quotient of degree-q cocycles by coboundaries in a cochain complex. Topological cohomology groups arise from singular or cellular cochains. Their direct sum carries the cohomology ring structure when equipped with the cup product.
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    • Cohomology class Cohomology group

Cohomology class ([z]∈Hq(C))

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Cohomology group
The equivalence class of a cocycle in a cochain complex, where adding a coboundary leaves its class unchanged.

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  1. Cohomology
  2. Algebraic topology
  3. Geometry and topology
  4. Area of mathematics
  5. Mathematics
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 Incoming links (3)

  • Boundary module
  • Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 114 / 1 / c / Solution
  • Quasi-isomorphism

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