The complex of end reductions of a contractible open 3-manifold: constructing 1-dimensional examples

Details The complex of end reductions of a contractible open 3-manifold: constructing 1-dimensional examples The complex of end reductions of a contractible open 3-manifold: constructing 1-dimensional examples

2004-05-19

arxiv.org/abs/math/0405380v1

Mathematics

Geometric Topology

23 pages, 3 figures, to appear in Boletin de la Sociedad Matematica Mexicana special issue (Ficofest Proceedings) in honor of

Scientific paper

Given an irreducible contractible open 3-manifold W which is not homeomorphic to R^3, there is an associated simplicial complex S(W), the complex of end reductions of W. Whenever W covers a 3-manifold M one has that the fundamental group of M is isomorphic to a subgroup of the group Aut(S(W)) of simplicial automorphisms of W. In this paper we give a new method for constructing examples W with S(W) isomorphic to a triangulation of R. It follows that any 3-manifold M covered by W must have infinite cyclic fundamental group. We also give a complete isotopy classification of the end reductions of W.

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