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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Involutions fixing ${\mathbb{RP}}^{\text{odd}} \sqcup P(h,i)$, II


Author: Zhi Lü
Journal: Trans. Amer. Math. Soc. 356 (2004), 1291-1314
MSC (2000): Primary 57R85, 57S17, 57R20, 55N22
Published electronically: October 29, 2003
MathSciNet review: 2034310
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Abstract: This paper studies the equivariant cobordism classification of all involutions fixing a disjoint union of an odd-dimensional real projective space ${\mathbb{RP}}^j$ with its normal bundle nonbounding and a Dold manifold $P(h,i)$ with $h$ a positive even and $i>0$. The complete analysis of the equivariant cobordism classes of such involutions is given except that the upper and lower bounds on the codimension of $P(h,i)$ may not be best possible. In particular, we find that there exist such involutions with nonstandard normal bundle to $P(h,i)$. Together with the results of part I of this title (Trans. Amer. Math. Soc. 354 (2002), 4539-4570), the argument for involutions fixing ${\mathbb{RP}}^{\text{odd}}\sqcup P(h,i)$ is finished.


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Additional Information

Zhi Lü
Affiliation: Institute of Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China
Address at time of publication: Department of Mathematics, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
Email: zlu@fudan.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03489-5
PII: S 0002-9947(03)03489-5
Keywords: Involution, Dold manifold, characteristic class
Received by editor(s): March 15, 2002
Published electronically: October 29, 2003
Additional Notes: This work was supported by grants from NSFC and JSPS (No. P02299)
Article copyright: © Copyright 2003 American Mathematical Society