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On the suspension order of

Authors:	Paul Silberbush Jack Ucci

Institution:	Department of Mathematics, Syracuse University, Syracuse, New York 13244 Jack Ucci ; Department of Mathematics, Syracuse University, Syracuse, New York 13244

Abstract:	It is shown that the suspension order of the -fold cartesian product $(RP^{2m})^{k]}$ of real projective -space $RP^{2m}$ is less than or equal to the suspension order of the -fold symmetric product $SP^{k}RP^{2m}$ of $RP^{2m}$ and greater than or equal to $2^{r+s+1}$ , where and 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 , 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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