Indecomposable $PD_3$-complexes

J. A. Hillman

doi:10.2140/agt.2012.12.131

paper

Indecomposable $P D_{3}$ -complexes

arXiv:0808.1775 · doi:10.2140/agt.2012.12.131

Abstract

We show that if $X$ is an indecomposable $P D_{3}$ -complex and $π_{1} (X) i s t h e f u n d am e n t a l g r o u p o f a r e d u ce df ini t e g r a p h o f f ini t e g r o u p s b u t i s n o t v i r t u a l l y cy c l i c t h e n$ X $i sor i e n t ab l e, t h e u n d er l y in g g r a p hi s a t r ee, a l l t h ee d g e g r o u p s a r e$ Z/2Z $an d a l l b u t a t m os t o n eo f t h e v er t e xg r o u p s i s d ih e d r a l o f or d er$ 2m $w i t h$ m $o dd . E v er y s u c h g r o u p i sr e a l i z e d b y so m e$ PD_3 $- co m pl e x . W e a l so p r o p ose a s t r a t e g y f or t a c k l in g t h e q u es t i o n o f w h e t h er e v er y$ PD_3$-complex has a finite covering space which is homotopy equivalent to a closed orientable 3-manifold.

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

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An indecomposable PD_3-complex : II

Indecomposable PD3​-complexes

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Indecomposable $P D_{3}$ -complexes