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ESTIMATING THE SIZE OF THE $(H, G)$-COINCIDENCES SET IN REPRESENTATION SPHERES

Part of: Classical Topics in Algebraic Topology

Published online by Cambridge University Press:  17 October 2022

D. DE MATTOS Open the ORCID record for D. DE MATTOS [Opens in a new window] ,
E. L. DOS SANTOS Open the ORCID record for E. L. DOS SANTOS [Opens in a new window]  and
T. O. SOUZA Open the ORCID record for T. O. SOUZA [Opens in a new window]
D. DE MATTOS
Affiliation:
Departamento de Matemática, Universidade de São Paulo-USP-ICMC, Caixa Postal 668, 13560-970 São Carlos-SP, Brazil e-mail: deniseml@icmc.usp.br
E. L. DOS SANTOS
Affiliation:
Departamento de Matemática, Universidade Federal de São Carlos, Centro de Ciências Exatas e Tecnologia, CP 676, CEP 13565-905 São Carlos-SP, Brazil e-mail: edivaldo@dm.ufscar.br
T. O. SOUZA*
Affiliation:
Faculdade de Matemática, Universidade Federal de Uberlândia, Campus Santa Mônica - Bloco 1F - Sala 1F120, Av. João Naves de Avila, 2121, Uberlândia, MG, CEP 38.408-100, Brazil
*
e-mail: tacioli@ufu.br
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Abstract

Let W be a real vector space and let V be an orthogonal representation of a group G such that $V^{G} = \{0\}$ (for the set of fixed points of G). Let $S(V)$ be the sphere of V and suppose that $f: S(V) \to W$ is a continuous map. We estimate the size of the $(H, G)$ -coincidences set if G is a cyclic group of prime power order $\mathbb {Z}_{p^k}$ or a p-torus $\mathbb {Z}_p^k$ .

Keywords

Borsuk–Ulam theorem(H,G)−coincidencerepresentation spheres

MSC classification

Primary: 55M20: Fixed points and coincidences
Secondary: 55M35: Finite groups of transformations (including Smith theory)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 2 , April 2023 , pp. 313 - 319
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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