The stable free rank of symmetry of products of spheres

TL;DR

This paper proves a conjecture in transformation group theory regarding free actions of elementary abelian p-groups on products of spheres, under conditions where p is large relative to the dimension.

Contribution

It establishes the conjecture for large primes p using tame homotopy theory, extending previous results to non-simply connected spaces.

Findings

Confirmed the conjecture for large primes p

Extended the theory to non-simply connected spaces

Utilized tame homotopy theory in the proof

Abstract

A well known conjecture in the theory of transformation groups states that if p is a prime and (Z/p)^r acts freely on a product of k spheres, then r is less than or equal to k. We prove this assertion if p is large compared to the dimension of the product of spheres. The argument builds on tame homotopy theory for non simply connected spaces.