Deformations of Whitehead Products, Symplectomorphism Groups, and Gromov–Witten Invariants

homotopy groups π∗(Xλ)⊗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 Ak map a multiple of a map f : S1 −→ 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 Xλ are classifying spaces of symplectomorphism groups BSymp( g × S2, ωλ) where ωλ is a symplectic deformation on the trivial ruled surface g × S2. Our method of detecting nontriviality is based on computations of equivariant Gromov–Witten in-