Homology, Homotopy and Applications

Volume 16 (2014)

Number 1

Free 2-rank of symmetry of products of Milnor manifolds

Pages: 65 – 81

DOI: http://dx.doi.org/10.4310/HHA.2014.v16.n1.a4

Author

Mahender Singh (Indian Institute of Science Education and Research, Mohali, Punjab, India)

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.

Keywords

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

2010 Mathematics Subject Classification

Primary 57S25. Secondary 55T10, 57S17.

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