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FREE ACTIONS OF SOME COMPACT GROUPS ON MILNOR MANIFOLDS

Part of: Fiber spaces and bundles Classical Topics in Algebraic Topology

Published online by Cambridge University Press:  31 October 2018

PINKA DEY  and
MAHENDER SINGH
PINKA DEY
Affiliation:
Department of Mathematical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, SAS Nagar, Manauli (PO), Punjab 140306, India e-mails: [email protected], [email protected]
MAHENDER SINGH
Affiliation:
Department of Mathematical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, SAS Nagar, Manauli (PO), Punjab 140306, India e-mails: [email protected], [email protected]
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Abstract

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In this paper, we investigate free actions of some compact groups on cohomology real and complex Milnor manifolds. More precisely, we compute the mod 2 cohomology algebra of the orbit space of an arbitrary free ℤ2 and $\mathbb{S}^1$-action on a compact Hausdorff space with mod 2 cohomology algebra of a real or a complex Milnor manifold. As applications, we deduce some Borsuk–Ulam type results for equivariant maps between spheres and these spaces. For the complex case, we obtain a lower bound on the Schwarz genus, which further establishes the existence of coincidence points for maps to the Euclidean plane.

MSC classification

Primary: 57S25: Groups acting on specific manifolds 57S10: Compact groups of homeomorphisms
Secondary: 55R20: Spectral sequences and homology of fiber spaces 55M20: Fixed points and coincidences
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 3 , September 2019 , pp. 727 - 742
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

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