|
|||||
|
|
|
|
|
|
|
|
|
A
parametrized Borsuk–Ulam theorem for a product of spheres
with free $\mathbb{Z}_p$–action and free $S^1$–action
Denise de Mattos and Edivaldo L dos Santos |
|
Algebraic & Geometric Topology 7 (2007) 1791–1804
|
Abstract |
|
In this paper, we prove parametrized Borsuk–Ulam theorems for bundles whose fibre has the same cohomology (mod ) as a product of spheres with any free –action and for bundles whose fibre has rational cohomology ring isomorphic to the rational cohomology ring of a product of spheres with any free –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 , we estimate the “size” of the –coincidence set of a fibre-preserving map. |
Keywords
parametrized Borsuk–Ulam theorem, characteristic
polynomials, free action, equivariant map, product of
spheres
|
Mathematical Subject Classification 2000
Primary: 55M20
Secondary: 55R91, 55R25
|
References |
Publication
Received: 5 February 2007
Revised: 2 October 2007
Accepted: 4 October 2007
Published: 18 December 2007
|
Authors |
| Denise de Mattos | |
| Departamento de Matemática Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo Caixa Postal 668 São Carlos, SP 13560-970 Brazil |
|
| http://www.icmc.usp.br/~topologia/ | |
| Edivaldo L dos Santos | |
| Departamento de Matemática Universidade Federal de São Carlos Caixa Postal 676 São Carlos, SP 13565-905 Brazil |
|
| http://www2.dm.ufscar.br/~edivaldo/ | |
|
