Small Cover and Halperin-Carlsson Conjecture

Abstract

We prove that the Halperin-Carlsson conjecture holds for any free (Z_2)^m action on a compact manifold whose orbit space is a small cover. In addition, we show that if the total space of a principal (Z_2)^m bundle over a small cover is connected, it must be equivalent to a partial quotient of the corresponding real moment-angle manifold with some canonical Z_2-torus action.

20 pages, 4 figure. The article is significantly expanded from the previous version, and some references are added

References in corpus (2)

• The stable free rank of symmetry of products of spheres
• Toral rank conjecture for moment-angle complexes