Bounded symplectic diffeomorphisms and split flux groups

TL;DR

This paper proves a conjecture about bounded symplectic diffeomorphisms for certain closed symplectic manifolds and shows how flux groups behave under products of these manifolds.

Contribution

It establishes the bounded isometry conjecture for a specific class of symplectic manifolds and describes the flux group's structure for their products.

Findings

Bounded isometry conjecture proven for a special class of symplectic manifolds.

Flux group of a product of these manifolds is isomorphic to the sum of individual flux groups.

Enhanced understanding of flux groups in symplectic geometry.

Abstract

We prove the bounded isometry conjecture of F. Lalonde and L. Polterovich for a special class of closed symplectic manifolds. As a byproduct, it is shown that the flux group of a product of these special symplectic manifold is isomorphic to the direct sum of the flux group of each symplectic manifold.