Remarks on invariants of hamiltonian loops

Abstract

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.

22 pages; cosmetic changes

References in corpus (2)

• Characteristic classes of smooth fibrations
• A characteristic number of bundles determined by mass linear pairs

Cited by in corpus (1)

• Polytopes with mass linear functions II: the 4-dimensional case