Knot Equivalence Through Braids and Rational Tangles

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dc.contributor.advisorRaines, Brian Edward, 1975-
dc.contributor.authorSchultze, Adam
dc.contributor.departmentMathematics.en_US
dc.contributor.schoolsHonors College.en_US
dc.date.accessioned2013-05-23T23:45:22Z
dc.date.available2013-05-23T23:45:22Z
dc.date.copyright2012-12
dc.date.issued2013-05-23
dc.description.abstractA major goal in the study of knot theory is to discover more practical and universal methods that determine knot equivalence. In this paper, we will explore two methods of doing so through the use of rational tangles and braids. We begin by determining a method of converting from knots to rational tangles, then find equivalence between the tangles by means of continued fractions and Prime Fractional Sets, and then convert the tangles back into knots. This leads to the conclusion that two knots have corresponding rational tangles which are equivalent if and only if the original two knots were themselves equivalent. Through a similar course of events, we then do the same with braids through the use of Markovs Moves and come to the conclusion of Markovs Theorem, where two knots are shown to be equivalent if and only if their corresponding braids are determined to be Markov equivalent.en_US
dc.identifier.urihttp://hdl.handle.net/2104/8630
dc.language.isoen_USen_US
dc.rightsBaylor University projects are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.en_US
dc.rights.accessrightsWorldwide accessen_US
dc.titleKnot Equivalence Through Braids and Rational Tanglesen_US
dc.typeThesisen_US

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