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We provide a new way of understanding the multiplicative structure of the rational homotopy groups π * (X λ ) ⊗ Q for a family of topological spaces, once we know enough about their additive structure. This allows us to interpret the condition of realizing as an A k map a multiple of a map f : S 1 −→ G between two topological groups in terms of the existence of a rational Whitehead product of order k. Our main example will be when the X λ are classifying spaces of symplectomorphism groupsdoi:10.1093/imrn/rnp215 fatcat:ul4i5b7whbgufinavdsaizc6ey