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UBC Theses and Dissertations
Skein modules and character varieties Clay, Adam Joseph
Abstract
We present a survey of the theory of skein modules of manifolds, and an introduction to skein algebras of groups. By applying a trick of Doug Bullock, we use SL(2, C) character varieties to highlight some infinite linearly independent families of knots in the Kauffman Bracket skein module of a 3-manifold. These families are composed of a knot K, together with all (1, n)-cablings of K. We also exhibit a method of explicit computation based upon the work of Robert Riley, which can identify infinite linearly independent families in the skein algebras of 2-bridge knot groups.
Item Metadata
| Title |
Skein modules and character varieties
|
| Creator | |
| Publisher |
University of British Columbia
|
| Date Issued |
2005
|
| Description |
We present a survey of the theory of skein modules of manifolds, and an introduction
to skein algebras of groups. By applying a trick of Doug Bullock, we
use SL(2, C) character varieties to highlight some infinite linearly independent
families of knots in the Kauffman Bracket skein module of a 3-manifold.
These families are composed of a knot K, together with all (1, n)-cablings of
K. We also exhibit a method of explicit computation based upon the work of
Robert Riley, which can identify infinite linearly independent families in the
skein algebras of 2-bridge knot groups.
|
| Genre | |
| Type | |
| Language |
eng
|
| Date Available |
2009-12-11
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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.
|
| DOI |
10.14288/1.0079409
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2005-11
|
| Campus | |
| Scholarly Level |
Graduate
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| Aggregated Source Repository |
DSpace
|
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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.