actions whose fixed data has a section
Author:
Pedro L. Q. Pergher
Journal:
Trans. Amer. Math. Soc. 353 (2001), 175189
MSC (2000):
Primary 57R85; Secondary 57R75
Published electronically:
June 21, 2000
MathSciNet review:
1783791
Fulltext PDF Free Access
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Abstract: Given a collection of real vector bundles over a closed manifold , suppose that, for some is of the form , where is the trivial onedimensional bundle. In this paper we prove that if is the fixed data of a action, then the same is true for the Whitney sum obtained from by replacing by . This stability property is wellknown for involutions. Together with techniques previously developed, this result is used to describe, up to bordism, all possible actions fixing the disjoint union of an even projective space and a point.
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Additional Information
Pedro L. Q. Pergher
Affiliation:
Departamento de Matemática, Universidade Federal de São Carlos, Caixa Postal 676, CEP 13.565905, São Carlos, SP, Brazil
Email:
pergher@dm.ufscar.br
DOI:
http://dx.doi.org/10.1090/S0002994700026453
PII:
S 00029947(00)026453
Keywords:
$(Z_{2})^{k}$action,
fixed data,
Stong's exact sequence,
$((Z_{2})^{k},q)$manifoldbundle,
projective space bundle,
bordism class,
representation,
Smith homomorphism
Received by editor(s):
November 11, 1998
Published electronically:
June 21, 2000
Additional Notes:
The present work was partially supported by CNPq
Article copyright:
© Copyright 2000
American Mathematical Society
