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Knots, tangles and braid actions Watson, Liam Thomas
Abstract
Recent work of Eliahou, Kauffmann and Thistlethwaite suggests the use of braid actions to alter a link diagram without changing the Jones polynomial. This technique produces non-trivial links (of two or more components) having the same Jones polynomial as the unlink. In this paper, examples of distinct knots that can not be distinguished by the Jones polynomial are constructed by way of braid actions. Moreover, it is shown in general that pairs of knots obtained in this way are not Conway mutants, hence this technique provides new perspective on the Jones polynomial, with a view to an important (and unanswered) question: Does the Jones polynomial detect the unknot?
Item Metadata
Title |
Knots, tangles and braid actions
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2004
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Description |
Recent work of Eliahou, Kauffmann and Thistlethwaite suggests the use of
braid actions to alter a link diagram without changing the Jones polynomial.
This technique produces non-trivial links (of two or more components) having
the same Jones polynomial as the unlink. In this paper, examples of distinct
knots that can not be distinguished by the Jones polynomial are constructed
by way of braid actions. Moreover, it is shown in general that pairs of knots
obtained in this way are not Conway mutants, hence this technique provides
new perspective on the Jones polynomial, with a view to an important (and
unanswered) question: Does the Jones polynomial detect the unknot?
|
Extent |
2473280 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-11-27
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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 |
10.14288/1.0080066
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2004-11
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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.