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 0→Ai→Bj→C→0
Connecting homomorphism map is
d∗:Hk(C)→Hk+1(A) - Then the short exact sequence of cochain complexes
0→Ai→Bj→C→0
gives rise to long exact sequence in cohomology.
⋯Hk−1(C)d∗→Hk(A)i∗→Hk(B)j∗→Hk(C)d∗→Hk+1(A)⋯
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