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You searched for +publisher:"University of Illinois – Chicago" +contributor:("Kauffman, Louis H."). Showing records 1 – 2 of 2 total matches.

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University of Illinois – Chicago

1. Simpson, David H. The Application of Ribbon Hopf Algebras to Invariants of 1-1 Tangles.

Degree: 2019, University of Illinois – Chicago

We examine the relation between Ribbon Hopf Algebras and 1-1 Tangles  – knot diagrams that are cut at a point with the ends pulled apart. Specifically, we investigate the behavior of one such algebra, introduced in the 1992 paper "On Kauffman’s knot invariants arising from finite-dimensional Hopf algebras" by David Radford. We compile the first-ever results for knots of 3-10 crossings using one of these algebras, and discuss the magnitude of calculations involved, and practical methods of attaining results in reasonable time. Advisors/Committee Members: Kauffman, Louis H (advisor), Radford, David (committee member), Shalen, Peter (committee member), Takloo-Bighash, Ramin (committee member), Licht, Arthur (committee member), Kauffman, Louis H (chair).

Subjects/Keywords: Knot Invariants; Hopf Algebras

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

APA (6th Edition):

Simpson, D. H. (2019). The Application of Ribbon Hopf Algebras to Invariants of 1-1 Tangles. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/23681

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):

Simpson, David H. “The Application of Ribbon Hopf Algebras to Invariants of 1-1 Tangles.” 2019. Thesis, University of Illinois – Chicago. Accessed July 10, 2020. http://hdl.handle.net/10027/23681.

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

MLA Handbook (7th Edition):

Simpson, David H. “The Application of Ribbon Hopf Algebras to Invariants of 1-1 Tangles.” 2019. Web. 10 Jul 2020.

Vancouver:

Simpson DH. The Application of Ribbon Hopf Algebras to Invariants of 1-1 Tangles. [Internet] [Thesis]. University of Illinois – Chicago; 2019. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/10027/23681.

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

Council of Science Editors:

Simpson DH. The Application of Ribbon Hopf Algebras to Invariants of 1-1 Tangles. [Thesis]. University of Illinois – Chicago; 2019. Available from: http://hdl.handle.net/10027/23681

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


University of Illinois – Chicago

2. 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 July 10, 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. 10 Jul 2020.

Vancouver:

Schneider J. Diagrammatic Theories of 1- and 2- Dimensional Knots. [Internet] [Thesis]. University of Illinois – Chicago; 2016. [cited 2020 Jul 10]. 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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