Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 11 of 11 for “"Jones polynomial"”.
-
On the Breadth of the Jones Polynomial for Certain Classes of Knots and Links
… Cr(K) of a knot or a link K by computing the Jones polynomial of K, V(K). The crossing number Cr(K) is bounded from below by the difference between the greatest degree and the smallest degree of the polynomial V(K). However the computation of the Jones polynomial of an arbitrary knot or link …
-
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 …
-
Knots, Skein Theory and q-Series
… the first n coefficients of P_n. The colored Jones polynomial is link invariant that associates to every link in S^3 a sequence of Laurent polynomials. In the first part of this work we study the tail of the unreduced colored Jones polynomial of alternating links using the colored Kauffman …
-
A Survey of Knot Theory
… developments in knot theory, for example the Jones polynomial, are also discussed, giving the reader the opportunity to see newer theory along with the old. We conclude by noting the incomplete state of affairs in knot theory: the lack of a perfect invariant.
-
A new structure on Khovanov's homology
… diagram. Khovanov invariant specializes to the Jones polynomial by taking graded Euler characteristic. Bar-Natan [1] [2] computed this invariant for the prime knots of up to 11 crossings. From the data, Bar-Natan, Garoufalidis, and Khovanov formulated two conjectures on the value of the Khovanov …
-
From Homological Algebra To Topology via Type B Zigzag Algebra and Heisenberg Algebra
… representation, and hence, a new presentation of Jones polynomial can be obtained.
-
From Homological Algebra To Topology via Type B Zigzag Algebra and Heisenberg Algebra
… representation, and hence, a new presentation of Jones polynomial can be obtained.
-
Knotting of optical vortices
… exhibit patterns in their Alexander and Jones polynomial coefficients, as well as in their Conway notation as parameters in the construction are varied. We use these patterns to propose a tabulation of the knots and links we can construct. The knots and links we can construct are examined …
-
A recursive formula for the Khovanov cohomology of a family of 3-stranded pretzel knots
After reviewing the process of associating graded cohomology groups (Khovanov cohomology) to a knot, we prove two lemmas that reduce the computational complexity of calculating the Khovanov cohomology. We then prove a recursive formula for the class of three-stranded pretzel knots P(-n,-m,m), where …
-
Entanglement, topology, & renormalization
… the Gauss linking number for Abelian links, and Jones polynomial for SU(2)). We will exhibit several examples of multi-component links in both the Abelian and the SU(2) theories, and afterwards discuss generic features of the entanglement of link states in Chern-Simons theories with a compact …