Dissertation/Thesis Abstract

Finite-Sheeted Covering Spaces and Solenoids over 3-manifolds
by Cavendish, Will, Ph.D., Princeton University, 2012, 96; 3522387
Abstract (Summary)

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 : SM 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 : SM, 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.

Indexing (document details)
Advisor: Gabai, David
Commitee: Browder, William, Fenley, Sergio, Gabai, David, Szabo, Zoltan
School: Princeton University
Department: Mathematics
School Location: United States -- New Jersey
Source: DAI-B 74/01(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Covering space, Manifolds, Solenoids
Publication Number: 3522387
ISBN: 978-1-267-54485-8
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