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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 35 for “"Knot Theory"”.
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A Survey of Knot Theory
… paper is to bring together a few topics in know theory. To discuss the classical branch of knot theory, where the not groups are defined, we make the necessary topological and algebraic developments. The van Kampen theorem is stated and used to find knot groups in the traditional way, and also in …
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A Comparison of Bayesian Regression Models Applied in Knot Theory
… used to estimate the mean box length of a random knot as a function of the number of edges of that knot. Specifically, this research recognizes uncertainty in box length variance and compares the resulting inference with that based on an approach that does not recognize such uncertainty. The …
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The Structure of the Cayley Complex and a Cubic-Time Algorithm for Solving the Conjugacy Problem for Groups of Prime Alternating Knots
… is helpful. The preface includes a history of knot theory and combinatorial group theory.
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Invariants of Legendrian links
… new, readily computable invariants of Legendrian knots and links in standard contact three-space, allowing us to answer many previously open questions in contact knot theory. The origin of these invariants is the powerful Chekanov-Eliashberg differential graded algebra, which we reformulate and …
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The Enhanced Linking Number and its Applications
A \emph{knot} is the image of an embedding of $S^1$ into $\R^3$, and a \emph{link} is the disjoint union of multiple knots. Most of the thesis is spent studying knots and two-component links. Knot theory is concerned with classifying knots and links, and we discuss three notions of equivalence. …
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Topology and geometry-based methods for quantifying the complexity of protein structures
New topological and geometrical methods in knot theory provide a way to rigorously measure the entanglement of open curves in 3-space for the first time. These methods enable the topological analysis of physical systems of filaments, such as those formed by proteins. In this dissertation we employ …
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Heegaard Floer Invariants and Cabling
A natural question in knot theory is to ask how certain properties of a knot behave under satellite operations. We will focus on the satellite operation of cabling, and on Heegaard Floer-theoretic properties. In particular, we will give a formula for the Ozsvath-Szabo concordance invariant tau of …
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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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Topological analysis of microtubules during cell division
… curves in space and use methods from Knot Theory to characterize the single and multi-chain topological complexity of such systems. We create computational methods for analyzing the topology of microtubules obtained through large electron tomography data. Our results show that the …
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Loop Edge Estimation in 4-Regular Hamiltonian Graphs
In knot theory, a knot is defined as a closed, non-self-intersecting curve embedded in three-dimensional space that cannot be untangled to produce a simple planar loop. A mathematical knot is essentially a conventional knot tied with rope where the ends of the rope have been glued together. One way …
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Constructing Hecke-type Structures, their Representations and Applications
… role of the Hecke algebra in the development of knot theory. More speci�cally we explicitly derive the HOMFLY and Jones polynomials.
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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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Circle-Valued Generating Family Invariants
<p>Legendrian knot theory is the study of topological knots and links that satisfy an additional, geometric condition. This condition, imposed by a contact structure, makes it possible for certain knots to be topologically equivalent without being Legendrian equivalent. In recent years, real-valued …
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Fractality and topology of optical singularities
… from experiments that generated compact vortex knots and links in real Gaussian beams. These results were achieved through the use of algebraic knot theory and random search optimisation algorithms. Finally, polarisation singularity densities are measured experimentally which confirm analytic …
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A survey of butterfly diagrams for knots and links
1 PDF file (ix, 93 pages)
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Kazhdan-Laumon Categories and Representations
… properties related to the representation theory of G and the geometry of the basic affine space G/U. In the first part of this thesis, we conduct an in-depth study of Kazhdan-Laumon categories from a modern perspective. We first define and study an analogue of the Bernstein-Gelfand-Gelfand …
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Quantum money and scalable 21-cm cosmology
… quantum money using techniques from knot theory. The second part of my thesis is about 21-cm cosmology and the Fast Fourier transform telescope. With the FFT telescope group at MIT, I worked on a design for a radio telescope that operates between 120 and 200 MHz and will scale to an …
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Kauffman Bracket Skein Modules And The Quantum Torus
… the definition is that if L [SUBSET OF] S 3 is a knot, then the (colored) Jones polynomials Jn (L) ∈ C[q ±1 ] can be computed from Kq (S 3 \ L). It was shown in [14] that Kq (T 2 x [0, 1]) ~ AZ2 , the subalgebra of the quantum =q torus XY = q 2 Y X which is invariant under the involution X …
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