Indecomposable PD3-complexes



We show that if the fundamental group π of an indecomposable PD3-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 PD3-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, PD3-complex, PD3-group, 3-manifold, virtually free.

AMS Subject Classification: Primary 57M25.

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Friday, August 15, 2008