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

 

$({\mathbb Z}_2)^k$-actions with $w(F)=1$


Author: Zhi Lü
Journal: Proc. Amer. Math. Soc. 133 (2005), 3721-3733
MSC (2000): Primary 57R85, 57S17, 55N22
Published electronically: June 8, 2005
MathSciNet review: 2163612
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Abstract: Suppose that $(\Phi, M^n)$ is a smooth $({\mathbb Z}_2)^k$-action on a closed smooth $n$-dimensional manifold such that all Stiefel-Whitney classes of the tangent bundle to each connected component of the fixed point set $F$ vanish in positive dimension. This paper shows that if $\dim M^n>2^k\dim F$ and each $p$-dimensional part $F^p$ possesses the linear independence property, then $(\Phi, M^n)$ bounds equivariantly, and in particular, $2^k\dim F$ is the best possible upper bound of $\dim M^n$ if $(\Phi, M^n)$ is nonbounding.


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Additional Information

Zhi Lü
Affiliation: Institute of Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China
Email: zlu@fudan.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07941-4
PII: S 0002-9939(05)07941-4
Keywords: $({\mathbb{Z}}_2)^k$-action, equivariant cobordism, linear independence condition
Received by editor(s): February 9, 2004
Received by editor(s) in revised form: July 25, 2004
Published electronically: June 8, 2005
Additional Notes: This work was supported by grants from NSFC (No. 10371020) and JSPS (No. P02299)
Dedicated: Dedicated to Professor Zhende Wu on his seventieth birthday
Communicated by: Paul Goerss
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.



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