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Khovanov Homology on Symmetric Unions of Certain 2-Bridge Knots

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Author
Gafney, T. .J.
Advisor
Jabuka, Stanislav
Date
2011
Type
Thesis
Department
Mathematics and Statistics
Degree Level
Honors Thesis
Degree Name
Mathematics
Statistics

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Abstract
Symmetric unions, originally introduced in 1957 by Shin’ichi Kinoshita and Hide- taka Terasaka [3], have since been studied due to their failure to be distinguished by some invariants. In his 2000 paper, Mikhail Khovanov introduced a powerful new invariant, Khovanov Homology, which gives more information (an entire homology) than some more classic invariants. In this paper, we look at Khovanov Homology’s ability to distinguish or classify symmetric unions of particular knots. We are able to show that Khovanov Homology can, in fact, classify symmetric unions of (2,m)-torus knots and certain other 2-bridge knots.
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http://hdl.handle.net/11714/558
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