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

2023/11/27 by Amelotte, Steven, Cutler, Tyrone, So, Tseleung
#55P15 #57N65 #57P10 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.16073

Abstract

Let X be a connected, orientable, 5-dimensional Poincaré duality complex with torsion-free H₁(X;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 π³(X) and π³(X;ℤ/k) as well as give partial information about the cohomotopy set π²(X).

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