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

 

On the suspension order of $(RP^{2m})^{[k]}$


Authors: Paul Silberbush and Jack Ucci
Journal: Proc. Amer. Math. Soc. 126 (1998), 1867-1872
MSC (1991): Primary 55P35; Secondary 55S15
MathSciNet review: 1443856
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Abstract: It is shown that the suspension order of the $k$-fold cartesian product $(RP^{2m})^{[k]}$ of real projective $2m$-space $RP^{2m}$ is less than or equal to the suspension order of the $k$-fold symmetric product $SP^{k}RP^{2m}$ of $RP^{2m}$ and greater than or equal to $2^{r+s+1}$, where $k$ and $m$ satisfy $2^{r} \le 2m < 2^{r+1}$ and $2^{s}\le k<2^{s+1}$. In particular $RP^{2} \times RP^{2}$ has suspension order $8$, and for fixed $m\ge 1$ the suspension orders of the spaces $(RP^{2m})^{[k]}$ are unbounded while their stable suspension orders are constant and equal to $2^{\phi (2m)}$.


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Additional Information

Paul Silberbush
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244

Jack Ucci
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244
Email: jjucci@tristano.syr.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04259-2
PII: S 0002-9939(98)04259-2
Received by editor(s): November 19, 1996
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1998 American Mathematical Society