Let X be a simplicial complex. For an (oriented) n-simplex of X, the coboundary n
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Let X be a simplicial complex. For an (oriented) n-simplex σ of X, the coboundary δn(σ) of σ is the (n + 1) chain ∑τ, where the sum is taken over all (n + 1)-simplexes τ that have σ as a face. That is, the simplexes τ appearing in the sum are precisely those that have σ as a summand of ∂n+ 1 (τ). Orientation is important here. Thus P2 is a face of P1P2, but P1 is not. However, P1 is a face of P2P1. Let X be the simplicial complex consisting of the solid tetrahedron of Fig. 41.2.
a. Compute δ(0)(P1) and , δ(0)(P4).
b. Compute ,δ(1)(P3P2).
c. Compute δ(2)(P3P2P4).
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