This thesis develops techniques for studying towers of finite-sheeted covering spaces of 3-manifolds. The central question we seek to address is the following: given a π1-injective continuous map ƒ : S → M of a 2-manifold S into a 3-manifold M, when does there exist a non-trivial connected finite-sheeted covering space M' of M such that ƒ lifts to M'? We approach this problem by reformulating it in terms of isometric actions of π1(M) on compact metric spaces. We then study regular solenoids over M, which give natural examples of compact metric spaces with isometric π 1(M)-actions. We conclude by introducing a construction that we call the mapping solenoid of a map ƒ : S → M, which can be used to derive cohomological criteria that guarantee the existence of a lift of ƒ to a non-trivial connected finite-sheeted covering space of M.
|Commitee:||Browder, William, Fenley, Sergio, Gabai, David, Szabo, Zoltan|
|School Location:||United States -- New Jersey|
|Source:||DAI-B 74/01(E), Dissertation Abstracts International|
|Keywords:||Covering space, Manifolds, Solenoids|
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