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September 10, 2025Transactions of the London Mathematical Society0 citationsOpen Access

Cohomotopy sets of (n−1) (n-1) ‐connected (2n+2) (2n+2) ‐manifolds for small nn

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PLPengcheng LiJPJianzhong PanJWJie Wu

Key Points

  • Cohomotopy sets are thoroughly explored for most cases of connected manifolds but not for the specific case studied.
  • The integration of Postnikov towers and homotopy decompositions reveals novel insights into these mathematical structures.
  • The assumption of 2-torsion-free homology is crucial for the analysis of these cohomotopy sets in the paper.
  • Investigations into these manifolds deepen the understanding of their topological properties, which have implications for broader mathematical theory.

Abstract

Abstract Let be a closed orientable ‐connected ‐manifold, . In this paper, we combine the Postnikov tower of spheres and the homotopy decomposition of the reduced suspension space to investigate the (integral) cohomotopy sets for , under the assumption that has 2‐torsion‐free homology. All cohomotopy sets of such manifolds are well‐understood except for .

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Cite This Study

Li et al. (2025) studied this question.

synapsesocial.com/papers/68c189ca9b7b07f3a0613014https://doi.org/10.1112/tlm3.70010
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