Free Torus Actions and Two-Stage Spaces

Abstract

We prove the toral rank conjecture of Halperin in some new cases. Our results apply to certain elliptic spaces that have a two-stage Sullivan minimal model, and are obtained by combining new lower bounds for the dimension of the cohomology and new upper bounds for the toral rank. The paper concludes with examples and suggestions for future work.Comment: 17 pages, to appear in Math. Proc. Camb. Philos. So