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$G$-coincidences for maps of homotopy spheres into CW-complexes

Authors: Daciberg L. Gonçalves, Jan Jaworowski and Pedro L. Q. Pergher
Journal: Proc. Amer. Math. Soc. 130 (2002), 3111-3115
MSC (1991): Primary 55M20; Secondary 55M35
Published electronically: March 12, 2002
MathSciNet review: 1908937
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Abstract: Let $G$ be a finite group acting freely in a CW-complex $\Sigma ^{m}$ which is a homotopy $m$-dimensional sphere and let $f:\Sigma ^{m} \to Y$ be a map of $\Sigma ^{m}$ to a finite $k$-dimensional CW-complex $Y$. We show that if $m\geq \vert G\vert k$, then $f$ has an $(H,G)$-coincidence for some nontrivial subgroup $H$ of $G$.

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Additional Information

Daciberg L. Gonçalves
Affiliation: Instituto de Matemática e Estatísca, Universidade de São Paulo, Rua do Matão, 1010, Agência Jardim Paulistano, Caixa Postal 66281, CEP 05315-970, São Paulo, SP, Brasil

Jan Jaworowski
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405-5701

Pedro L. Q. Pergher
Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, Rodovia Washington Luiz, km 235, Caixa Postal 676, CEP 13.565-905, São Carlos, SP, Brasil

Keywords: $G$-coincidence, $G$-equivariant, polyhedron, $G$-action, transfer, generalized Gysin sequence.
Received by editor(s): December 14, 2000
Received by editor(s) in revised form: May 10, 2001
Published electronically: March 12, 2002
Additional Notes: The first author was partially supported by CNPq and FAPESP and the third author was partially supported by CNPq
Communicated by: Paul Goerss
Article copyright: © Copyright 2002 American Mathematical Society