End reductions and covering spaces of contractible open 3-manifolds

Details End reductions and covering spaces of contractible open 3-manifolds End reductions and covering spaces of contractible open 3-manifolds

2002-09-29

arxiv.org/abs/math/0209397v1

Mathematics

Geometric Topology

58 pages, 10 figures

Scientific paper

This paper uses Brin and Thickstun's theory of end reductions of non-compact 3-manifolds to study groups of covering translations of irreducible contractible open 3-manifolds W which are not homeomorphic to R^3. We associate to W an object S(W) called the simplicial complex of minimal R^2-irreducible end reductions of W. Whenever W covers another 3-manifold the group of covering translations is isomorphic to a fixed point free group of automorphisms of S(W). We apply this result to give uncountably many examples of R^2-irreducible such W which cover 3-manifolds with infinite cyclic fundamental group and non-trivially cover only 3-manifolds with infinite cyclic fundamental group. We also give uncountably many examples of R^2-irreducible W which are not eventually end irreducible and do not non-trivially cover any 3-manifold.

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