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https://hdl.handle.net/2440/62680
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DC Field | Value | Language |
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dc.contributor.advisor | Murray, Michael | en |
dc.contributor.advisor | Varghese, Mathai | en |
dc.contributor.author | Roberts, David Michael | en |
dc.date.issued | 2010 | en |
dc.identifier.uri | http://hdl.handle.net/2440/62680 | - |
dc.description.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. | en |
dc.subject | category theory; groupoids; algebraic topology; homotopy theory | en |
dc.title | Fundamental bigroupoids and 2-covering spaces. | en |
dc.type | Thesis | en |
dc.contributor.school | School of Mathematical Sciences : Pure Mathematics | en |
dc.description.dissertation | Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2010 | en |
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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