Free Circle Actions on the Product of Three Spheres

2025/05/28 by Hemant Kumar Singh, Dimpi, Singh, Hemant Kumar
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Primary 57S17 #Secondary 57S25

paper · pdf · doi:10.48550/arxiv.2505.21993

openalex publication_date 2025/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The orbit spaces of free S⁰-actions on the mod 2 cohomology product of three spheres, Sⁿ x S^m x S^l, 1 <= n <= m <= l have been determined in [6]. In this paper, we extend these findings to free S¹-actions on the rational cohomology product of three spheres. This extension also builds upon the work of Dotzel et al. [7], who studied free circle actions on the rational cohomology product of two spheres. Additionally, we establish Borsuk-Ulam type theorems.

Citations

• Orbit spaces of free involutions on the product of three spheres
• Fixed point Free Actions of Spheres and Equivariant maps
• Fixity and Free Group Actions on Products of Spheres

Related

• Orbit spaces of free involutions on the product of three spheres
• Fixed point Free Actions of Spheres and Equivariant maps
• Fixed point sets and orbit spaces of wedge of three spheres
• Cohomology Classification of Spaces with Free S3 Actions
• Free circle actions on certain simply connected 7-manifolds