On actions of tori and quaternionic tori on products of spheres

Abstract

In this paper we study the actions of tori (standard compact tori, as well as their quaternionic analogues) on products of spheres. It is proved that the orbit space of a specific action of a torus on a product of spheres is homeomorphic to a sphere. A similar statement for a real torus ${\mathbb{Z}}_2^n$ was proved by the second author in 2019. We also provide a statement about arbitrary compact topological groups, generalizing the mentioned results, as well as the results of the first author about the actions of a compact torus of complexity one.

arXiv comment10 pages

References in corpus (5)

• On the orbit space of a compact linear Lie group with commutative connected component
• Torus actions of complexity one and their local properties
• Branched coverings of simply connected manifolds
• Orbit spaces of equivariantly formal torus actions of complexity one
• Equivariantly formal 2-torus actions of complexity one