Suspension splittings of 5-dimensional Poincaré duality complexes and their applications
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 $π^2(X)$.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Geometry and complex manifolds
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Algebraic & Geometric Topology
- Volume
- 26
- Issue
- 1
- Pages
- 283–319
- Publication date
- 16 January 2026
- Language
- EN