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University of Illinois – Chicago

1. Schneider, Jonathan. Diagrammatic Theories of 1- and 2- Dimensional Knots.

Degree: 2016, University of Illinois – Chicago

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. Advisors/Committee Members: Kauffman, Louis H. (advisor), Radford, David (committee member), Takloo-Bighash, Ramin (committee member), Licht, Arthur L. (committee member), Culler, Marc (committee member).

Subjects/Keywords: knot theory; knot diagrams; surface knot theory; 2-knot theory; virtual knots; virtual knot theory; welded knots

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Schneider, J. (2016). Diagrammatic Theories of 1- and 2- Dimensional Knots. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/20811

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Schneider, Jonathan. “Diagrammatic Theories of 1- and 2- Dimensional Knots.” 2016. Thesis, University of Illinois – Chicago. Accessed August 06, 2020. http://hdl.handle.net/10027/20811.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Schneider, Jonathan. “Diagrammatic Theories of 1- and 2- Dimensional Knots.” 2016. Web. 06 Aug 2020.

Vancouver:

Schneider J. Diagrammatic Theories of 1- and 2- Dimensional Knots. [Internet] [Thesis]. University of Illinois – Chicago; 2016. [cited 2020 Aug 06]. Available from: http://hdl.handle.net/10027/20811.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Schneider J. Diagrammatic Theories of 1- and 2- Dimensional Knots. [Thesis]. University of Illinois – Chicago; 2016. Available from: http://hdl.handle.net/10027/20811

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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