The complex of end reductions of a contractible open 3-manifold: constructing 1-dimensional examples
Abstract
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.
Cite
@article{arxiv.math/0405380,
title = {The complex of end reductions of a contractible open 3-manifold: constructing 1-dimensional examples},
author = {Robert Myers},
journal= {arXiv preprint arXiv:math/0405380},
year = {2007}
}
Comments
23 pages, 3 figures, to appear in Boletin de la Sociedad Matematica Mexicana special issue (Ficofest Proceedings) in honor of Francisco Gonzalez-Acuna