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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


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