Mathematics – Symplectic Geometry
Scientific paper
2009-05-11
Mathematics
Symplectic Geometry
22 pages; cosmetic changes
Scientific paper
In this note the interrelations between several natural morphisms on the $\pi_1$ of groups of Hamiltonian diffeomorphisms are investigated. As an application, the equality of the (non-linear) Maslov index of loops of quantomorphisms of prequantizations of $\C P^n$ and the Calabi-Weinstein invariant is shown, settling affirmatively a conjecture by A. Givental. We also prove the proportionality of the mixed action-Maslov morphism and the Futaki invariant on loops of Hamiltonian biholomorphisms of Fano Kahler manifolds, as suggested by C. Woodward. Finally, a family of generalized action-Maslov invariants is computed for toric manifolds via barycenters of their moment polytopes, with an application to mass-linear functions recently introduced by D. McDuff and S. Tolman.
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