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Title: Finite-Sheeted Covering Spaces and Solenoids over 3-manifolds
Authors: Cavendish, William Palmer
Advisors: Gabai, David
Contributors: Mathematics Department
Keywords: 3-manifold
Covering Space
Subjects: Mathematics
Issue Date: 2012
Publisher: Princeton, NJ : Princeton University
Abstract: 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 π_1-injective continuous map f: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 f lifts to M'? We approach this problem by reformulating it in terms of isometric actions of π_1(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 f:S → M, which can be used to derive cohomological criteria that guarantee the existence of a lift of f to a non-trivial connected finite-sheeted covering space of M.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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