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 ℤp–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 = ℤp, we estimate the “size” of the ℤp–coincidence set of a fibre-preserving map.
de Mattos, Denise 1 ; dos Santos, Edivaldo 2
@article{10_2140_agt_2007_7_1791,
author = {de Mattos, Denise and dos Santos, Edivaldo},
title = {A parametrized {Borsuk{\textendash}Ulam} theorem for a product of spheres with free {\ensuremath{\mathbb{Z}}p{\textendash}action} and free {S1{\textendash}action}},
journal = {Algebraic and Geometric Topology},
pages = {1791--1804},
year = {2007},
volume = {7},
number = {4},
doi = {10.2140/agt.2007.7.1791},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2007.7.1791/}
}
TY - JOUR AU - de Mattos, Denise AU - dos Santos, Edivaldo TI - A parametrized Borsuk–Ulam theorem for a product of spheres with free ℤp–action and free S1–action JO - Algebraic and Geometric Topology PY - 2007 SP - 1791 EP - 1804 VL - 7 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2007.7.1791/ DO - 10.2140/agt.2007.7.1791 ID - 10_2140_agt_2007_7_1791 ER -
%0 Journal Article %A de Mattos, Denise %A dos Santos, Edivaldo %T A parametrized Borsuk–Ulam theorem for a product of spheres with free ℤp–action and free S1–action %J Algebraic and Geometric Topology %D 2007 %P 1791-1804 %V 7 %N 4 %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2007.7.1791/ %R 10.2140/agt.2007.7.1791 %F 10_2140_agt_2007_7_1791
de Mattos, Denise; dos Santos, Edivaldo. A parametrized Borsuk–Ulam theorem for a product of spheres with free ℤp–action and free S1–action. Algebraic and Geometric Topology, Tome 7 (2007) no. 4, pp. 1791-1804. doi: 10.2140/agt.2007.7.1791
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