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A combinatorial approach to the exponents of Moore spaces

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Abstract

In this article, we give a combinatorial approach to the exponents of Moore spaces. Our result states that the projection of the \(p^{r+1}\)-power map of the loop space of the \((2n+1)\)-dimensional mod \(p^r\) Moore space to its atomic piece containing the bottom cell \(T^{2n+1}\{p^r\}\) is null homotopic for \(n>1\), \(p>3\) and \(r>1\). This result strengthens the classical result that \(\Omega T^{2n+1}\{p^r\}\) has an exponent \(p^{r+1}\).

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Notes

  1. The notion of relative exponent is suggested by the referee.

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Acknowledgements

The authors would like to gratefully thank F. Petrov for discussions related to the subject of the paper. We wish to thank the referee most warmly for numerous suggestions that have improved the exposition of this paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Rochester, Rochester, NY, 14625, USA

    Frederick R. Cohen

  2. Chebyshev Laboratory, St. Petersburg State University, 14th Line, 29b, Saint Petersburg, 199178, Russia

    Roman Mikhailov

  3. St. Petersburg Department of Steklov Mathematical Institute, Saint Petersburg, Russia

    Roman Mikhailov

  4. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore, 119076, Singapore

    Jie Wu

Authors
  1. Frederick R. Cohen
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  2. Roman Mikhailov
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  3. Jie Wu
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Corresponding author

Correspondence to Jie Wu.

Additional information

The main result (Theorem 1.1) is supported by Russian Scientific Foundation, Grant no. 14-21-00035. J. Wu is also partially supported by the Singapore Ministry of Education research Grant (AcRF Tier 1 WBS no. R-146-000-222-112) and a Grant (no. 11329101) of NSFC of China.

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Cohen, F.R., Mikhailov, R. & Wu, J. A combinatorial approach to the exponents of Moore spaces. Math. Z. 290, 289–305 (2018). https://doi.org/10.1007/s00209-017-2018-5

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