Free 2-rank of symmetry of products of Milnor manifolds

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.

Keywords

free rank, Milnor manifold, Leray-Serre spectral sequence, Steenrod algebra

2010 Mathematics Subject Classification

Primary 57S25. Secondary 55T10, 57S17.

Full Text (PDF format)

Published 2 June 2014