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

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- by Paul Silberbush and Jack Ucci
- Proc. Amer. Math. Soc.
**126**(1998), 1867-1872 - DOI: https://doi.org/10.1090/S0002-9939-98-04259-2
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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 $2^{\phi (2m)}$.## References

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## Bibliographic 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
- Received by editor(s): November 19, 1996
- Communicated by: Thomas Goodwillie
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**126**(1998), 1867-1872 - MSC (1991): Primary 55P35; Secondary 55S15
- DOI: https://doi.org/10.1090/S0002-9939-98-04259-2
- MathSciNet review: 1443856