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On modular cohomotopy groups

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Abstract

Let p be a prime and let πn(X; ℤ/pr) = [X, Mn(ℤ/pr)] be the set of homotopy classes of based maps from CW-complexes X into the mod pr Moore spaces Mn(ℤ/pr) of degree n, where ℤ/pr denotes the integers mod pr. In this paper we firstly determine the modular cohomotopy groups πn(X; ℤ/pr) up to extensions by classical methods of primary cohomology operations and give conditions for the splitness of the extensions. Secondly we utilize some unstable homotopy theory of Moore spaces to study the modular cohomotopy groups; especially, the group π3(X; ℤ(2)) with dim(X) ≤ 6 is determined.

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Authors and Affiliations

  1. Department of Mathematics, Southen University of Science and Technology, Shenzhen, 518055, P. R. China

    Pengcheng Li

  2. Institute of Mathematics, Chinese Academy of Mathematics and Systems Science, University of Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Jianzhong Pan

  3. School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024, P. R. China

    Jie Wu

  4. Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, 101408, P. R. China

    Jie Wu

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  1. Pengcheng Li
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  2. Jianzhong Pan
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  3. Jie Wu
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Correspondence to Jie Wu.

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Li, P., Pan, J. & Wu, J. On modular cohomotopy groups. Isr. J. Math. 253, 887–915 (2023). https://doi.org/10.1007/s11856-022-2409-0

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  • DOI: https://doi.org/10.1007/s11856-022-2409-0

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