On actions of tori and quaternionic tori on products of spheres

2023/09/11 by Anton Ayzenberg, Ayzenberg, Anton, Dmitry Vladimirovich Gugnin +1
Mathematics · #57S12 #57S15 #57S25 (Primary) 57R10 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2309.05611

openalex publication_date 2023/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ℤ₂ⁿ 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.

Related

• Quotients of Spheres By Linear Actions of Tori
• Toric orbit spaces which are manifolds
• Equivariantly formal 2-torus actions of complexity one
• The topology of local quaternionic toric actions
• Orbit spaces of equivariantly formal torus actions of complexity one