Manuscript III-B@1 · III-B-v1.tex · lemma · d2c98f62

Lemma: Poisson compensation

The unchanged-product obstruction › The chart Poisson prescription · lines 669–685 · proof included or linked

III-B@1#lem:poisson

For $ξ \in C_{c}^{\infty} (I \times B_{r_{*}}; T^{*})$ ,

w_{P}^{μ} [h + K ξ] = w_{P}^{μ} [h] - ξ^{μ} .

Proof. Direct differentiation gives

A_{i} [K ξ] = Δ ξ_{i}, B [K ξ] = Δ ξ_{0} .

Use Newton inversion, $ξ^{i} = ξ_{i}$ , and $ξ^{0} = - ξ_{0}$ .

Displayed formulas in this passage