End Reductions and Covering Translations of Contractible Open 3-manifolds
نویسنده
چکیده
This paper uses Brin and Thickstun’s theory of end reductions of noncompact 3-manifolds to study groups of covering translations of irreducible contractible open 3-manifolds W which are not homeomorphic to R. We associate to W an object S(W ) called the simplicial complex of minimal R-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-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-irreducible W which are not eventually end irrreducible and do not non-trivially cover any 3-manifold.
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