## Indecomposable *PD*_{3}-complexes

### J.A.Hillman

#### Abstract

We show that if the fundamental group *π* of an
indecomposable *PD*_{3}-complex is the fundamental
group of a finite graph of finite groups then the vertex groups
have periodic cohomology and the edge groups are metacyclic. If
the vertex groups all have cohomological period dividing 4 then
they are dihedral, the edge groups are *Z/2Z* and the
underlting graph is a tree. We also ask whether every
*PD*_{3}-complex has a finite covering space which
is homotopy equivalent to a closed orientable 3-manifold, and
suggest a strategy for proving this.

Keywords:
degree-1 map, Dehn surgery, graph of groups, normalizer,

*PD*_{3}-complex,

*PD*_{3}-group, 3-manifold, virtually free.

AMS Subject Classification:
Primary 57M25.