Multisymplectic actions of compact Lie groups on spheres

TL;DR

This paper explores the existence of homotopy comoment maps for high-dimensional spheres with multisymplectic structures, focusing on compact Lie group actions and providing explicit constructions in key cases.

Contribution

It solves the existence problem for homotopy comoment maps on spheres under compact group actions and offers explicit examples in notable scenarios.

Findings

Existence of homotopy comoment maps on spheres established.

Explicit constructions provided for specific group actions.

Results advance understanding of multisymplectic geometry on spheres.

Abstract

We investigate the existence of homotopy comoment maps (comoments) for high-dimensional spheres seen as multisymplectic manifolds. Especially, we solve the existence problem for compact effective group actions on spheres and provide explicit constructions for such comoments in interesting particular cases.