## $$PD_3$$-complexes bound

### Jonathan A. Hillman

#### Abstract

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.

: Primary 57M45; secondary 57P10.

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 Saturday, November 27, 2021