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

2025/02/21 by Stanton, Lewis, Theriault, Stephen · 1 citation
#57R19 #Algebraic Topology (math.AT) #FOS: Mathematics #Primary 55P35

paper · doi:10.48550/arxiv.2502.15385

Abstract

Under certain hypotheses, we prove a loop space decomposition for simply-connected Poincaré Duality complexes of dimension n whose (n-1)-skeleton is a co-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)-skeleton and describe its homology as a one-relator algebra.

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