$P{D}_3$-complexes bound

Jonathan A. Hillman

Abstract

We show that every $P{D}_3$-complex $P$ bounds a $P{D}_4$-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, $P{D}_3$-group, ${\pi }_1$-injective.

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