# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1906.08790