Example 0. In the last section we have proved, using the gluing identity, that the **data** Q : Q d = ϕ ! (π * b T (V d )) associated with a mixed bundle V and a multiplicative class b T satisfies the Euler **data** identity. This indicates that the gluing identity is really the geometric origin of Euler data. This is what motivates our definition of Euler data. Note that since Q d is the equivariant push-forward of a class in H * G (M d (X)), the polynomial condition on Q is automatic. This condition will be needed when mirror transformation is discussed.  
P d = − c 1 (L),d −1 k=1 (L + kα)
is an Ω-Euler **data** where Ω = c 1 (L) −1 .