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2007 A parametrized Borsuk–Ulam theorem for a product of spheres with free $\mathbb{Z}_p$–action and free $S^1$–action
Denise de Mattos, Edivaldo dos Santos
Algebr. Geom. Topol. 7(4): 1791-1804 (2007). DOI: 10.2140/agt.2007.7.1791

Abstract

In this paper, we prove parametrized Borsuk–Ulam theorems for bundles whose fibre has the same cohomology (mod p) as a product of spheres with any free p–action and for bundles whose fibre has rational cohomology ring isomorphic to the rational cohomology ring of a product of spheres with any free S1–action. These theorems extend the result proved by Koikara and Mukerjee in [A Borsuk–Ulam type theorem for a product of spheres, Topology Appl. 63 (1995) 39–52]. Further, in the particular case where G=p, we estimate the “size” of the p–coincidence set of a fibre-preserving map.

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Denise de Mattos. Edivaldo dos Santos. "A parametrized Borsuk–Ulam theorem for a product of spheres with free $\mathbb{Z}_p$–action and free $S^1$–action." Algebr. Geom. Topol. 7 (4) 1791 - 1804, 2007. https://doi.org/10.2140/agt.2007.7.1791

Information

Received: 5 February 2007; Revised: 2 October 2007; Accepted: 4 October 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 05221960
MathSciNet: MR2366178
Digital Object Identifier: 10.2140/agt.2007.7.1791

Subjects:
Primary: ‎55M20
Secondary: 55R25 , 55R91

Keywords: characteristic polynomials , equivariant map , free action , parametrized Borsuk–Ulam theorem , product of spheres

Rights: Copyright © 2007 Mathematical Sciences Publishers

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