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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$ Z_2^2$-actions with $ n$-dimensional fixed point set


Author: Pedro L. Q. Pergher
Journal: Proc. Amer. Math. Soc. 136 (2008), 1855-1860
MSC (2000): Primary 57R85; Secondary 57R75
Published electronically: December 21, 2007
MathSciNet review: 2373617
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Abstract: We describe the equivariant cobordism classification of smooth actions $ (M^m,\Phi)$ of the group $ G=Z_2^2$, considered as the group generated by two commuting involutions, on closed smooth $ m$-dimensional manifolds $ M^m$, for which the fixed point set of the action is a connected manifold of dimension $ n$ and $ m=4n-1$ or $ 4n-2$. For $ m \ge 4n$, the classification is known.


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Additional Information

Pedro L. Q. Pergher
Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, Caixa Postal 676, São Carlos, SP 13565-905, Brazil
Email: pergher@dm.ufscar.br

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09021-1
PII: S 0002-9939(07)09021-1
Keywords: $Z_2^2$-action, fixed data, equivariant cobordism class, characteristic number, projective space bundle, Stiefel-Whitney class.
Received by editor(s): September 1, 2006
Received by editor(s) in revised form: November 20, 2006
Published electronically: December 21, 2007
Additional Notes: The author was partially supported by CNPq and FAPESP
Communicated by: Paul Goerss
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.