We shall often apply the following version:
W d ω e κ ζ = 0 r d X i * r ω v e H ζ + H ζ ,r α . Definition 4.1. Fix an invertible class Ω ∈ H * T (X) −1 . A list P : P d ∈ H * G (W d ) −1 , d ≻ 0, is a Ω-Euler **data** if on X, Ω i * r P v d = i * 0 P v r i * 0 P v d−r
(called Euler **data** identity) for all r d, and the W d P d · ω are polynomial in α for all ω ∈ R d . By convention we set P 0 = Ω.