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Description
Title: | Alternating Quadrisecants of Knots |
Author(s): | Denne, Elizabeth Jane |
Doctoral Committee Chair(s): | Sullivan, John M. |
Department / Program: | Mathematics |
Discipline: | Mathematics |
Degree Granting Institution: | University of Illinois at Urbana-Champaign |
Degree: | Ph.D. |
Genre: | Dissertation |
Subject(s): | Mathematics |
Abstract: | The Main Theorem shows that every nontrivial tame knot in R3 has an alternating quadrisecant. This result refines the previous work about quadrisecants and gives greater geometric insight into knots. The Main Theorem provides new proofs to two previously known theorems about the total curvature and second hull of knotted curves. Moreover, essential alternating quadrisecants may be used to dramatically improve the known lower bounds on the ropelength of thick knots. |
Issue Date: | 2004 |
Type: | Text |
Language: | English |
Description: | 119 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004. |
URI: | http://hdl.handle.net/2142/86830 |
Other Identifier(s): | (MiAaPQ)AAI3130908 |
Date Available in IDEALS: | 2015-09-28 |
Date Deposited: | 2004 |
This item appears in the following Collection(s)
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Dissertations and Theses - Mathematics
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Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois