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


Author: Zhi Lü
Journal: Trans. Amer. Math. Soc. 354 (2002), 4539-4570
MSC (2000): Primary 57R85, 57S17, 57R20, 55N22
DOI: https://doi.org/10.1090/S0002-9947-02-02937-9
Published electronically: June 24, 2002
MathSciNet review: 1926888
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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 $h>0$ and $i>0$. For odd $h$, the complete analysis of the equivariant cobordism classes of such involutions is given except that the upper and lower bounds on codimension of $P(h,i)$ may not be best possible; for even $h$, the problem may be reduced to the problem for even projective spaces.


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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: https://doi.org/10.1090/S0002-9947-02-02937-9
Keywords: Involution, Dold manifold, characteristic class
Received by editor(s): July 12, 2000
Published electronically: June 24, 2002
Additional Notes: This work was supported by the scholar fund of the Ministry of Education in China and partially by the Japanese Government Scholarship
Article copyright: © Copyright 2002 American Mathematical Society

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