Loop spaces of 𝑛-dimensional Poincaré duality complexes whose (𝑛-1)-skeleton is a co-𝐻-space

Source 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.