-actions whose fixed data has a section

Author:
Pedro L. Q. Pergher

Journal:
Trans. Amer. Math. Soc. **353** (2001), 175-189

MSC (2000):
Primary 57R85; Secondary 57R75

DOI:
https://doi.org/10.1090/S0002-9947-00-02645-3

Published electronically:
June 21, 2000

MathSciNet review:
1783791

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a collection of real vector bundles over a closed manifold , suppose that, for some is of the form , where is the trivial one-dimensional 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 well-known 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 13.565-905, São Carlos, SP, Brazil

Email:
pergher@dm.ufscar.br

DOI:
https://doi.org/10.1090/S0002-9947-00-02645-3

Keywords:
$(Z_{2})^{k}$-action,
fixed data,
Stong's exact sequence,
$((Z_{2})^{k},q)$-manifold-bundle,
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