$P{D}_3$-complexes bound

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, and that if the inclusion of $Z$ into $P$ induces an isomorphism on fundamental groups then ${\pi }_1(Z)$ is a free group.

v2: Proof of Theorem 1 elaborated. New Theorem 2, on $P{D}_3$-complexes with manifold 1-skeleta; the original \S3 now an appendix. v3: new section, extending a theorem of Daverman to the $P{D}_4$-context. v4: appendix deleted, \S4 moved to follow \S1. Other minor changes. v5: exposition of Theorem 1, Lemma 3 and Theorem 4 tightened

References in corpus (1)

• Uncountably many groups of type $FP$