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UBC Theses and Dissertations
Finite subset spaces of the circle Rose, Simon
Abstract
In this thesis we investigate a new and highly geometric approach to studying finite subset spaces of the circle. By considering the circle as the boundary of the hyperbolic plane, we are able to use the full force of hyperbolic geometry—in particular, its well-understood group of isometries—to determine explicitely the structure of the first few configuration spaces of the circle S¹. Once these are understood we then move onto studying their union—that is, exp₃(S¹,)—and in particular, we re-prove both an old theorem of Bott and a newer (unpublished) result of E . Щепин (E. Shchepin) about this space.
Item Metadata
Title |
Finite subset spaces of the circle
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2007
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Description |
In this thesis we investigate a new and highly geometric approach to studying finite
subset spaces of the circle. By considering the circle as the boundary of the hyperbolic
plane, we are able to use the full force of hyperbolic geometry—in particular, its well-understood
group of isometries—to determine explicitely the structure of the first few
configuration spaces of the circle S¹. Once these are understood we then move onto
studying their union—that is, exp₃(S¹,)—and in particular, we re-prove both an old
theorem of Bott and a newer (unpublished) result of E . Щепин (E. Shchepin) about
this space.
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Genre | |
Type | |
Language |
eng
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Date Available |
2011-03-10
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080474
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.