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