Given a closed monotone symplectic manifold , we define certain characteristic cohomology classes of the free loop space with values in , and their equivariant version. These classes generalize the Seidel representation and satisfy versions of the axioms for Chern classes. In particular there is a Whitney sum formula, which gives rise to a graded ring homomorphism from the ring , with its Pontryagin product to with its quantum product. As an application we prove an extension to higher dimensional geometry of the loop space of a theorem of McDuff and Slimowitz on minimality in the Hofer metric of a semifree Hamiltonian circle action.
"Quantum characteristic classes and the Hofer metric." Geom. Topol. 12 (4) 2277 - 2326, 2008. https://doi.org/10.2140/gt.2008.12.2277