Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-98-04259-2
MathSciNet review: 1443856
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. M. Barratt, Spaces of finite characteristic, Quart. J. Math. Oxford 11 (1960), 124-136. MR 22:11396
  • 2. R. Bott and H. Samelson, On the Pontrjagin product in spaces of paths, Comment. Math. Helv 27 (1953), 320-337. MR 15:643b
  • 3. G. Bredon, Introduction to compact transformation groups, Academic Press, New York, 1972. MR 54:1265
  • 4. F.R. Cohen, J.C. Moore, and J.A. Neisendorfer, Exponents in homotopy theory, Algebraic Topology and Algebraic K-theory, Annals of Mathematics Studies, vol. 113, Princeton University Press, Princeton, 1987, pp. 3-71. MR 89d:55035
  • 5. J.L. Dupont and G. Lusztig, On manifolds satisfying $w_{1}^{2} = 0$, Topology 10 (1971), 81-92. MR 42:8508
  • 6. J. Mukai, A note on the Kahn-Priddy map, J. Math. Soc. Japan 40 (1988), 51-61. MR 88m:55018
  • 7. -, A remark on Toda's result about the suspension order of the stunted real projective space, Mem. Fac. Sci. Kyushu Univ. A 42 (1988), 87-94. MR 89j:55009
  • 8. P. Silberbush, Suspension orders and cartesian products, Preprint.
  • 9. H. Toda, Order of the identity class of a suspension space, Ann. of Math. 78 (1963), 300-325. MR 27:6271

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 55P35, 55S15

Retrieve articles in all journals with MSC (1991): 55P35, 55S15


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

American Mathematical Society