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Sunday, July 19, 2020

Cohomolgy-Long exact sequence

So far the following maps are defined.
  • Cochain map ϕ:Hk(A)Hk(B) induced cohomology map
    ϕ:Hk(A)Hk(B)
  • For short exact sequence of cochain complexes 0AiBjC0
    Connecting homomorphism map is
    d:Hk(C)Hk+1(A)
  • Then the short exact sequence of cochain complexes
    0AiBjC0
    gives rise to long exact sequence in cohomology.
    Hk1(C)dHk(A)iHk(B)jHk(C)dHk+1(A)

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