New constructions of symplectically fat fiber bundles

TL;DR

This paper introduces novel methods for constructing symplectically fat fiber bundles using the Kirwan map and isotropy representations, expanding the toolkit for symplectic geometry and fiber bundle theory.

Contribution

It presents new construction techniques for symplectically fat fiber bundles based on the Kirwan map and isotropy representations, providing fresh approaches in symplectic geometry.

Findings

New constructions of symplectically fat fiber bundles using the Kirwan map.

Expressing fatness condition via isotropy representation.

Applications to homogeneous spaces and G-structures.

Abstract

This work is devoted to new constructions of symplectically fat fiber bundles. The latter are constructed in two ways: using the Kirwan map and expressing the fatness condition in terms of the isotropy representation related to the G-structure over some homogeneous spaces.