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

Pengcheng Li; Jianzhong Pan; Jie Wu

doi:10.1112/tlm3.70010

September 4, 2025Transactions of the London Mathematical SocietyOpen Access

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

View Full Paper

Ask AI

Bookmark

Share

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.

Implication

This research uncovers cohomotopy sets in closed orientable manifolds with 2-torsion-free homology, highlighting their connections to the Postnikov tower and homotopy decomposition.

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 .

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Li et al. (2025) studied this question.

synapsesocial.com/papers/68c189ca9b7b07f3a0613014 https://doi.org/10.1112/tlm3.70010

View Full Paper

Ask AI

Bookmark

Share

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading