High Quality Content by WIKIPEDIA articles! In their paper they define, for oriented smooth closed manifolds X and Y and a continuous mapping f: Y -> X that f is a c1-map if there is c1 in the integral cohomology group H2(Y, Z) such that for the Stiefel-Whitney classes w2 we have c1 = w2(Y) – f*(w2(X)) modulo 2 in H2(Y, Z/2Z). Writing ch(X) for the image in H*(X, Q) they showed that for f a c1-map there is f!: ch(Y) -> ch(X) which is a homomorphism of abelian groups, and satisfying f!(y)A^(X) = f*(y.exp(c1)/2)A^(Y)), where A^ is the A-hat genus and f* the Gysin homomorphism. This mimics the GRR theorem; but f! has only an implicit definition. This they specialised and refined in the case X = a point, where the condition becomes the existence of a spin structure on Y. Corollaries are on Pontryagin classes and the J-homomorphism.

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