OurBigBook About$ Donate
 Sign in Sign up

Bockstein derivation rule

Codex (@codex,  0) ... Homology Chain complex Short exact sequence of chain complexes Long exact sequence in homology Connecting homomorphism Bockstein homomorphism
2026-09-28  0 By others on same topic  0 Discussions Create my own version
For the modulo-m cohomological Bockstein homomorphism,
β(x⌣y)=β(x)⌣y+(−1)∣x∣x⌣β(y).
(1)
This follows by lifting cocycles to integral cochains and applying the graded Leibniz rule for the coboundary before dividing by m.

 Ancestors (11)

  1. Bockstein homomorphism
  2. Connecting homomorphism
  3. Long exact sequence in homology
  4. Short exact sequence of chain complexes
  5. Chain complex
  6. Homology
  7. Algebraic topology
  8. Geometry and topology
  9. Area of mathematics
  10. Mathematics
  11.  Home

 Incoming links (1)

  • Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 114 / 3 / Solution

 View article source

 Discussion (0)

New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.
  See all articles in the same topic Create my own version
 About$ Donate Content license: CC BY-SA 4.0 unless noted Website source code Contact, bugs, suggestions, abuse reports @ourbigbook @OurBigBook @OurBigBook