Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/62680
Type: | Thesis |
Title: | Fundamental bigroupoids and 2-covering spaces. |
Author: | Roberts, David Michael |
Issue Date: | 2010 |
School/Discipline: | School of Mathematical Sciences : Pure Mathematics |
Abstract: | This thesis introduces two main concepts: a fundamental bigroupoid of a topological groupoid and 2-covering spaces, a categorification of covering spaces. The first is applied to the second to show, among other things, that the fundamental 2-group of the 2-covering space is a sub-2-group of the fundamental 2-group of the base. Along the way we derive general results about localisations of the 2-categories of categories and groupoids internal to a site at classes of weak equivalences, construct a topological fundamental bigroupoid of locally well-behaved spaces, and finish by providing a rich source of examples of 2-covering spaces, including a functorial 2-connected 2-covering space. |
Advisor: | Murray, Michael Varghese, Mathai |
Dissertation Note: | Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2010 |
Keywords: | category theory; groupoids; algebraic topology; homotopy theory |
Appears in Collections: | Research Theses |
Files in This Item:
File | Description | Size | Format | |
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01front.pdf | 93.34 kB | Adobe PDF | View/Open | |
02whole.pdf | 1.35 MB | Adobe PDF | View/Open |
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