Following the idea of Exercise 10, let X be a simplicial complex, and let the group C
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Following the idea of Exercise 10, let X be a simplicial complex, and let the group C(n)(X) of n-cochains be the same as the group Cn(X).
a. Define δ(n) : C(n)(X) → C(n+1)(X) in a way analogous to the way we defined ∂n: Cn(X) → Cn-1(X).
b. Show that ∂2 = 0, that is, that ,∂(n+1)∂n(c)) = 0 for each c ∈ C(n)(X).
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a We define n C n C n1 by b It suffices to show that n1 n 0 for e...View the full answer
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