Indecomposable $PD_3$-complexes

J. A. Hillman

doi:10.2140/agt.2012.12.131

Indecomposable $PD_3$-complexes

Geometric Topology 2014-07-22 v4 Algebraic Topology

Authors: J. A. Hillman

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Abstract

We show that if $X$ is an indecomposable $PD_3$ -complex and $\pi_1(X) is the fundamental group of a reduced finite graph of finite groups but is not virtually cyclic then$ X $is orientable, the underlying graph is a tree, all the edge groups are$ Z/2Z $and all but at most one of the vertex groups is dihedral of order$ 2m $with$ m $odd. Every such group is realized by some$ PD_3 $-complex. We also propose a strategy for tackling the question of whether every$ PD_3$-complex has a finite covering space which is homotopy equivalent to a closed orientable 3-manifold.

Keywords

manifolds mapping class groups homotopy groups

Cite

@article{arxiv.0808.1775,
  title  = {Indecomposable $PD_3$-complexes},
  author = {J. A. Hillman},
  journal= {arXiv preprint arXiv:0808.1775},
  year   = {2014}
}

Comments

22 pages. The determination of the possible fundamental groups has been completed. A lemma has been added to Section 2, and the main theorem (5.2) has been strengthened

Indecomposable $PD_3$-complexes

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