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arXiv · 2311.16073

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

Steven Amelotte·Tyrone Cutler·Tseleung So
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Abstract

Let $X$ be a connected, orientable, 5-dimensional Poincaré duality complex with torsion-free $H_1(X;\mathbb{Z})$. We show that $ΣX$ 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 $π^3(X;\mathbb{Z}/k)$ as well as give partial information about the cohomotopy set $π^2(X)$.

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Steven Amelotte, Tyrone Cutler, Tseleung So. 2024-01-17. Suspension splittings of 5-dimensional Poincaré duality complexes and their applications. https://doi.org/10.2140/agt.2026.26.283

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