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Diagrammatic Theories of 1- and 2- Dimensional Knots

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posted on 01.07.2016, 00:00 by Jonathan Schneider
A meta-theory is described whereby any diagrammatic knot theory may be defined by specifying diagrams and moves. This is done explicitly in dimensions 1 and 2, with more abstract indication of how to extend the meta-theory to higher dimensions. Several examples are given in dimensions 1 and 2, with information about how the theories are related. A topological model for each theory is described. Particular focus is placed on virtual knot theory and welded knot theory, building on work by Kauffman, Satoh, and Rourke, with new results about Rourke's model of welded knots.

History

Advisor

Kauffman, Louis H.

Department

Mathematics

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Committee Member

Radford, David Takloo-Bighash, Ramin Licht, Arthur L. Culler, Marc

Submitted date

2016-05

Language

en

Issue date

01/07/2016

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