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Homotopy string links over surfaces Yurasovskaya, Ekaterina
Abstract
In his 1947 work "Theory of Braids" Emil Artin asked whether the braid group remained unchanged when one considered classes of braids under linkhomotopy, allowing each strand of a braid to pass through itself but not through other strands. We generalize Artin's question to string links over orientable surface M and show that under link-homotopy surface string links form a group PBn(M), which is isomorphic to a quotient of the surface pure braid group PBn(M). Surface braid groups and their properties are an area of active research by González-Meneses, Paris and Rolfsen, Goçalves and Guaschi, and our work explores the geometric and visual beauty of this subject. We compute a presentation of PBn(M) in terms of the generators and relations and discuss the orderability of the group in the case when the surface in question is a unit disk D.
Item Metadata
Title |
Homotopy string links over surfaces
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2008
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Description |
In his 1947 work "Theory of Braids" Emil Artin asked whether the braid
group remained unchanged when one considered classes of braids under linkhomotopy,
allowing each strand of a braid to pass through itself but not
through other strands. We generalize Artin's question to string links over
orientable surface M and show that under link-homotopy surface string links
form a group PBn(M), which is isomorphic to a quotient of the surface pure
braid group PBn(M). Surface braid groups and their properties are an area
of active research by González-Meneses, Paris and Rolfsen, Goçalves and
Guaschi, and our work explores the geometric and visual beauty of this
subject. We compute a presentation of PBn(M) in terms of the generators
and relations and discuss the orderability of the group in the case when the
surface in question is a unit disk D.
|
Extent |
1252099 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2008-11-03
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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 |
10.14288/1.0066783
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2008-11
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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