Manuscript III@2 · III.tex · section · 82dad3e5

Formal cancellation is not unchanged-product descent

What instantaneous Poisson compensation establishes › Formal cancellation is not unchanged-product descent · lines 2310–2341

Consider the active formal variation

δ_{ξ} h = K ξ + κ L_{ξ} h, δ_{ξ} ϕ = κ X_{ξ} ϕ .

On smooth configurations in the compensator domain,

δ_{ξ} F^{P}_{κ} = O (κ^{2})

formally, because

δ_{ξ} \int f ϕ = κ \int f X_{ξ} ϕ

and the leading variation of the correction is

κ \int f X_{w_{P} (K ξ)} ϕ = - κ \int f X_{ξ} ϕ .

This varies the scalar. The map $q_{0}$ does not. The varied scalar also need not remain free. Neither negative theorem is contradicted.

In coefficient notation, the cancellation is

δ_{0} F_{1} + δ_{1} F_{0} = 0,

not $δ_{0} F_{1} = 0$ .

Displayed formulas in this passage