\(PD_3\)-complexes bound

Jonathan A. Hillman


We show that every \(PD_3\)-complex \(P\) bounds a \(PD_4\)-pair \((Z,P)\). If \(P\) is orientable we may assume that \(\pi_1(Z)=1\). We show also that if \(P\) has a manifold 1-skeleton then it is homotopy equivalent to a closed 3-manifold.

Keywords: aspherical, boundary, fibration, \(PD_3\)-group, \(\pi_1\)-injective.

AMS Subject Classification: Primary 57M45; secondary 57P10.

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Saturday, November 27, 2021