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. / Science, Faculty of / Mathematics, Department of / Graduate
Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/2747 |
Date | 11 1900 |
Creators | Yurasovskaya, Ekaterina |
Publisher | University of British Columbia |
Source Sets | University of British Columbia |
Language | English |
Detected Language | English |
Type | Text, Thesis/Dissertation |
Format | 1252099 bytes, application/pdf |
Rights | Attribution-NonCommercial-NoDerivatives 4.0 International, http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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