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Showing 1 to 20 of 176 for “"Knots"”.
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Knots Not for Naught
… polynomial for each knot in a specific family of knots. This family of knots is generated from placing the Whitehead link into a solid torus, slicing the torus at a spot where the Whitehead has no crossings and then twisting the torus 360 degrees in either direction an integral number of times. …
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Alternating Quadrisecants of Knots
… 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 …
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Curves, Knots, and Total Curvature
We present an exposition of various results dealing with the total curvature of curves in Euclidean 3-space. There are two primary results: Fenchel's theorem and the theorem of Fary and Milnor. Fenchel's theorem states that the total curvature of a simple closed curve is greater than or equal to …
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On Nullification of Knots and Links
… of a type of local crossing change on oriented knots and links called nullification.</p> <p>One can define a distance between types of knots and links based on the minimum number of nullification moves necessary to change one to the other. Nullification distances form a class of isotopy …
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Knots, Skein Theory and q-Series
The tail of a sequence {P_n(q)} of formal power series in Z[q^{-1}][[q]], if it exists, is the formal power series whose first $n$ coefficients agree up to a common sign with the first n coefficients of P_n. The colored Jones polynomial is link invariant that associates to every link in S^3 a …
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Enumeration and classification of ribbon knots
… differ by twists along imbedded bands. When the knots under consideration possess a hyperbolic structure, we use a limiting process to show that a given knot can only be obtained in finitely many ways by adding twists to a suitably chosen ribbon. The resulting families of ribbons yield, even for …
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Bordered Legendrian knots and sutured Legendrian invariants
… variants of Floer homology to study Legendrian knots. First, given a front diagram for a Legendrian knot K in S₃ which has been split into several pieces, we associate a differential graded algebra to each "bordered" piece and prove a van Kampen theorem which recovers the Chekanov-Eliashberg …
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Obstructions to slicing knots and splitting links
… the unlink. In the second half, we consider knots as potential cross-sections of surfaces in R4. We use Heegaard Floer homology to show that certain knots never occur as cross-sections of surfaces with small first Betti number. (It was previously thought possible that every knot was a …
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The head and tail conjecture for alternating knots
The colored Jones polynomial is an invariant of knots and links, which produces a sequence of Laurent polynomials. In this work, we study new power series link invariants, derived from the colored Jones polynomial, called its head and tail. We begin with a brief survey of knot theory and the …
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Hypercube diagrams for knots, links, and knotted tori
… is a cube diagram of size n for K. Examples of knots for which the cube number detects chirality are presented. There is also a Legendrian version of this invariant called the Legendrian cube number. We will show that the Legendrian cube number distinguishes the Legendrian left hand torus knots …
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A survey of butterfly diagrams for knots and links
1 PDF file (ix, 93 pages)
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On Isotopy Types of Complexes With Application to Knots
Made available in DSpace on 2014-12-09T22:17:45Z (GMT). No. of bitstreams: 1 6901319.pdf: 1000956 bytes, checksum: 0ecc3e8baaad80e448e6d13e66f06332 (MD5) Previous issue date: 1967
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Precision X-ray spectroscopy of 3C 273 jet knots
… ([delta lambda] = 0.01A) spectra of 3C 273 jet knots extracted from eight observations made using Chandra in conjunction with the HETGS. Using these spectra we searched for narrow emission line candidates and, based on significance values calculated for the observed photon counts in each bin of …
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Higher Dimensional Convex Brunnian Links and Other Explorations in Knots
… Convex Brunnian Links and Other Explorations in Knots. Thesis under the direction of Hugh N. Howards, Ph.D., Associate Professor of Mathematics. This thesis will examine two areas of knot theory. The first involves stick numbers of knot, or the minimum number of straight line segments required to …
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Khovanov Homology on Symmetric Unions of Certain 2-Bridge Knots
… or classify symmetric unions of particular knots. We are able to show that Khovanov Homology can, in fact, classify symmetric unions of (2,m)-torus knots and certain other 2-bridge knots.
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Slice implies mutant ribbon for odd 5-stranded pretzel knots
… the infinite family of odd 3-stranded pretzel knots. In their work, they give a complete characterization of the slice/ribbon knots in that infinite family. This dissertation is motivated by their work and proves that the family of odd 5-stranded pretzel knots satisfiesa weaker version of the …
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Geometry-driven filamentary structures : elastic gridshells, weaves, clasps, and knots
… triaxial weaves, elastic clasps, and elastic knots. These studies involve a combination of geometric reasoning, high-fidelity numerical simulations, and precision model experiments using scale-invariance and advanced imaging techniques (e.g., 3D laser scanning, and X-ray computed tomography). …
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A Program to Visualize Legendrian Knots and Links from Generating Families
No abstract prepared.
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