 Cohomology class of the diagonal

ID: cohomology-class-of-the-diagonal

Let

M

be a closed oriented

n

e_{p, i}

be a homogeneous basis of

H^{p} (M; Q)

, and choose its Poincare-dual basis

e_{p, i}^{*} \in H^{n - p} (M; Q)

⟨ e_{p, i} e_{p, j}^{*}, [M]⟩ = δ_{ij}

. With the product-orientation convention, the Poincare dual of the diagonal is

ε_{Δ} = \sum_{p, i} (- 1)^{n p} e_{p, i}^{*} \times e_{p, i} .

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