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End reductions and covering spaces of contractible open 3-manifolds | Robert Myers
; | Date: |
29 Sep 2002 | Subject: | Geometric Topology MSC-class: 57M10, 57N10 | math.GT | Affiliation: | Oklahoma State University | Abstract: | 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. | Source: | arXiv, math.GT/0209397 | Services: | Forum | Review | PDF | Favorites |
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