Free 2-rank of symmetry of products of Milnor manifolds

Abstract

A real Milnor manifold is the non-singular hypersurface of degree (1,1) in the product of two real projective spaces. These manifolds were introduced by Milnor to give generators for the unoriented cobordism algebra, and they admit free actions by elementary abelian 2-groups. In this paper, we obtain some results on the free 2-rank of symmetry of products of finitely many real Milnor manifolds under the assumption that the induced action on mod 2 cohomology is trivial. Similar results are obtained for complex Milnor manifolds that are defined analogously. Here the free 2-rank of symmetry of a topological space is the maximal rank of an elementary abelian 2-group that acts freely on that space.