Suspension splittings of 5-dimensional Poincaré duality complexes and their applications

Amelotte, Steven; Cutler, Tyrone; So, Tseleung

doi:10.2140/agt.2026.26.283

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Suspension splittings of $5$-dimensional Poincaré duality complexes and their applications

Steven Amelotte, Tyrone Cutler and Tseleung So

Algebraic & Geometric Topology 26 (2026) 283–319

DOI: 10.2140/agt.2026.26.283

Abstract

Let $X$ be a connected, orientable, 5-dimensional Poincaré duality complex with torsion-free $H_{1} (X; ℤ)$ . We show that $Σ X$ is homotopy equivalent to a wedge of recognisable spaces and study to what extent its homotopy type is determined by algebraic data. These results are then used to compute the unstable cohomotopy groups $π^{3} (X)$ and $π^{3} (X; ℤ ∕ k)$ as well as give partial information about the cohomotopy set $π^{2} (X)$ .

Keywords

suspension splitting, Poincaré duality complex, 5-manifold, cohomotopy group

Mathematical Subject Classification

Primary: 55P15, 57N65, 57P10

References

Publication

Received: 17 January 2024

Revised: 9 January 2025

Accepted: 23 January 2025

Published: 16 January 2026

Authors

Steven Amelotte
School of Mathematics and Statistics Carleton University Ottawa, ON Canada

Tyrone Cutler
Beijing Institute of Mathematical Sciences and Applications Beijing China

Tseleung So
Institute of Mathematical Science Pusan National University Busan South Korea

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Volume 26, issue 1 (2026)