Khovanov Homology on Symmetric Unions of Certain 2-Bridge Knots
type: CreativeWork
description: 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.
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.
author: Gafney, T. .J.
language: en_US
language: English
date published: 2011
date modified: 2026-07-27T21:48:09Z
provider: University of Nevada - Reno
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Nevada, Reno

PropertyValue
property ID: Handle
value: http://hdl.handle.net/11714/558