Journal of Symplectic Geometry

Volume 18 (2020)

Number 6

Multisymplectic actions of compact Lie groups on spheres

Pages: 1751 – 1785



Antonio Michele Miti (Department of Mathematics, KU Leuven, Belgium; and Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Brescia, Italy)

Leonid Ryvkin (Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université de Paris, France)


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.

Received 10 July 2019

Accepted 6 December 2019

Published 2 February 2021