Khovanov Homology on Symmetric Unions of Certain 2-Bridge Knots

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.

Name thesis:degree_name

Mathematics

Level thesis:degree_level

Honors Thesis

Grantor

University of Nevada, Reno

Year dc:date.issued

2011

Author dc:creator

• Gafney, T. .J.

Advisor dc:contributor.advisor

• Jabuka, Stanislav

Statement dc:rights

• In Copyright(All Rights Reserved)

Language dc:language.iso

en_US, English

Handle dc:identifier.uri

http://hdl.handle.net/11714/558

OAI identifier oai:identifier

oai:scholarwolf.unr.edu:11714/558