On compositions of the loop and suspension functors
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- by M. H. Eggar PDF
- Proc. Amer. Math. Soc. 123 (1995), 597-606 Request permission
Abstract:
The problem studied is whether, from knowledge of the homotopy type of ${\Omega ^{{d_k}}}{\Sigma ^{{c_k}}} \cdots {\Omega ^{{d_2}}}{\Sigma ^{{c_2}}}{\Omega ^{{d_1}}}{\Sigma ^{{c_1}}}X = MX$ for suitable spaces X, one can recover the nonnegative integers ${c_1},{d_1}, \ldots ,{c_k},{d_k}$. The Betti numbers of X and ${c_1},{d_1}, \ldots ,{c_k},{d_k}$ do determine the ith Betti number of MX, but even for small k , i and for X a sphere (say) the answer is a complicated one, since it depends on parities and graded Witt numbers depending on graded Witt numbers. It is shown that k can be found and that ${c_i},{d_j}$ can always be determined up to finitely many possibilities and usually uniquely.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 597-606
- MSC: Primary 55P65; Secondary 55P62
- DOI: https://doi.org/10.1090/S0002-9939-1995-1218114-3
- MathSciNet review: 1218114