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Loop Numbers of Knots and Links

This thesis introduces a new quantity called loop number, and shows the conditions in which loop numbers become knot invariants. For a given knot diagram D, one can traverse the knot diagram and count the number of loops created by the traversal. The number of loops recorded depends on the starting point in the diagram D and on the traversal direction. Looking at the minimum or maximum number of loops over all starting points and directions, one can define two positive integers as loop numbers of the diagram D. In this thesis, the conditions under which these loop numbers become knot invariants are identified. In particular, the thesis answers the question when these numbers are invariant under flypes in the diagram D.

Identiferoai:union.ndltd.org:WKU/oai:digitalcommons.wku.edu:theses-2958
Date01 April 2017
CreatorsPham, Van Anh
PublisherTopSCHOLAR®
Source SetsWestern Kentucky University Theses
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceMasters Theses & Specialist Projects

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