Loop spaces of 𝑛-dimensional Poincaré duality complexes whose (𝑛-1)-skeleton is a co-𝐻-space
Abstract
Under certain hypotheses, we prove a loop space decomposition for simply-connected Poincaré Duality complexes of dimension n n whose ( n − 1 ) (n-1) -skeleton is a co- H H -space. This unifies many known decompositions obtained in different contexts and establishes many new families of examples. As consequences, we show that such a looped Poincaré Duality complex retracts off the loops of its ( n − 1 ) (n-1) -skeleton and describe its homology as a one-relator algebra.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Homotopy and Cohomology in Algebraic Topology
Geometry and complex manifolds
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 379
- Issue
- 4
- Pages
- 2683–2715
- Publication date
- 5 January 2026
- Language
- EN