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

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 .

Authors

Jie Wu (ORCID: https://orcid.org/0000-0003-2445-6750)
Pengcheng Li (ORCID: https://orcid.org/0000-0003-3845-3796)
Jianzhong Pan

Institutions

Dongguan University of Technology (CN)
Academy of Mathematics and Systems Science (CN)
Research Applications (United States) (US)
Hebei Normal University (CN)

Publication Details

Journal: Transactions of the London Mathematical Society
Published: 2025-09-04
DOI: https://doi.org/10.1112/tlm3.70010
Primary Topic: Homotopy and Cohomology in Algebraic Topology
Type: article
Field-Weighted Citation Impact: 0.00

Funders

National Natural Science Foundation of China

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article

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

Jie Wu, Pengcheng Li, Jianzhong Pan

Sep 4, 2025

Transactions of the London Mathematical Society

Homotopy and Cohomology in Algebraic Topology

article

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

Jie Wu, Pengcheng Li, Jianzhong Pan

September 4, 2025article en

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 .

Transactions of the London Mathematical SocietyVol. 12(1)

Dongguan University of Technology (CN), Academy of Mathematics and Systems Science (CN), Research Applications (United States) (US), Hebei Normal University (CN)

National Natural Science Foundation of China

Openalex Percentile: Top 70%

Homotopy and Cohomology in Algebraic Topology

DOI Open Access PDF OpenAlex

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