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UBC Theses and Dissertations
The space of left orderings of a group with applications to topology Clay, Adam J.
Abstract
A group is left orderable if there exists a strict total ordering of its elements that is invariant under multiplication from the left. The set of all left orderings of a group comes equipped with a natural topological structure and group action, and is called the space of left orderings. This thesis investigates the topology of the space of left orderings for a given group, by analyzing those left orderings that correspond to isolated points and by characterizing the orbits of the natural group action using maps from a certain free object. Lastly, we find an application of the space of left orderings in the field of 3-manifold topology, by using compactness to show that certain fundamental groups are not left orderable.
Item Metadata
| Title |
The space of left orderings of a group with applications to topology
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
2010
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| Description |
A group is left orderable if there exists a strict total ordering of its elements that is invariant under multiplication from the left. The set of all left orderings of a group comes equipped with a natural topological structure and group action, and is called the space of left orderings. This thesis investigates the topology of the space of left orderings for a given group, by analyzing those left orderings that correspond to isolated points and by characterizing the orbits of the natural group action using maps from a certain free object. Lastly, we find an application of the space of left orderings in the field of 3-manifold topology, by using compactness to show that certain fundamental groups are not left orderable.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2010-04-16
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0069888
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2010-05
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| Campus | |
| Scholarly Level |
Graduate
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International