Multisymplectic actions of compact Lie groups on spheres
Symplectic Geometry
2025-11-06 v2 Mathematical Physics
Differential Geometry
Group Theory
math.MP
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.
Cite
@article{arxiv.1906.08790,
title = {Multisymplectic actions of compact Lie groups on spheres},
author = {Antonio Michele Miti and Leonid Ryvkin},
journal= {arXiv preprint arXiv:1906.08790},
year = {2025}
}
Comments
26 pages; Corrected and added some references to the literature, especially regarding the cohomological obstructions to the existence of comoments in multisymplectic geometry. The abstract and introduction are changed accordingly, laying more focus on the second part of the publication. Implemented several minor revisions related to typos and inconsistencies in notation