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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 Solenoid |

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. |

URI: | http://arks.princeton.edu/ark:/88435/dsp01gx41mh898 |

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 |

Files in This Item:

File | Description | Size | Format | |
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Cavendish_princeton_0181D_10232.pdf | 623.84 kB | Adobe PDF | View/Download |

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