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Bourgin–Yang version of
the Borsuk–Ulam theorem for $\mathbb{Z}_{p^k}$–equivariant
maps
Wacław Marzantowicz, Denise de Mattos and Edivaldo L dos Santos |
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Algebraic & Geometric Topology 12 (2012) 2245–2258
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Abstract |
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Let be a cyclic group of prime power order and let and be orthogonal representations of with . Let be the sphere of and suppose is a –equivariant mapping. We give an estimate for the dimension of the set in terms of and . This extends the Bourgin–Yang version of the Borsuk–Ulam theorem to this class of groups. Using this estimate, we also estimate the size of the –coincidences set of a continuous map from into a real vector space . |
Keywords
equivariant maps, covering dimension, orthogonal
representation, equivariant $K$–theory
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Mathematical Subject Classification 2010
Primary: 55M20
Secondary: 55M35, 55N91, 57S17
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References |
Publication
Received: 30 April 2012
Revised: 14 August 2012
Accepted: 27 August 2012
Published: 5 January 2013
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Authors |
| Wacław Marzantowicz | |
| Faculty of Mathematics and Computer
Science Adam Mickiewicz University of Poznań ul. Umultowska 87 61-614 Poznań Poland |
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| Denise de Mattos | |
| Instituto de Ciências Matemáticas e
de Computação Departamento de Matemática Universidade de São Paulo Caixa Postal 668 13560-970 São Carlos Brazil |
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| http://www.icmc.usp.br/~topologia/ | |
| Edivaldo L dos Santos | |
| Departamento de Matemática Universidade Federal de São Carlos Caixa Postal 676 13565-905 São Carlos Brazil |
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| http://www2.dm.ufscar.br/~edivaldo/ | |
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