Free Circle Actions on the Product of Three Spheres

TL;DR

This paper extends the classification of free circle actions from products of two spheres to three spheres in rational cohomology, and establishes related Borsuk-Ulam type theorems, advancing understanding of symmetry actions on sphere products.

Contribution

It generalizes previous results by classifying free S^1-actions on the rational cohomology product of three spheres and introduces Borsuk-Ulam type theorems for these actions.

Findings

Classified orbit spaces of free S^1-actions on S^n x S^m x S^l in rational cohomology.

Extended previous work from two spheres to three spheres.

Established Borsuk-Ulam type theorems for these actions.

Abstract

The orbit spaces of free S^0-actions on the mod 2 cohomology product of three spheres, S^n x S^m x S^l, 1 <= n <= m <= l have been determined in [6]. In this paper, we extend these findings to free S^1-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.