Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 4 of 4
Full-Text Articles in Entire DC Network
On The Skein Theory Of 0-Framed Surgery Along The Trefoil Knot, Andrew Robert Holmes
On The Skein Theory Of 0-Framed Surgery Along The Trefoil Knot, Andrew Robert Holmes
LSU Doctoral Dissertations
In this dissertation, we will give a generating set of the Kauffman bracket skein module over the field Q(A) of 0-framed surgery along the trefoil knot. This generating set is described as a certain subset of a known basis for the skein module over Z[A^±1] of the trefoil exterior.
Obstructions To Embedding Genus-1 Tangles In Links, Susan Marie Abernathy
Obstructions To Embedding Genus-1 Tangles In Links, Susan Marie Abernathy
LSU Doctoral Dissertations
Given a compact, oriented 3-manifold M in S3 with boundary, an (M,2n)-tangle T is a 1-manifold with 2n boundary components properly embedded in M. We say that T embeds in a link L in S3 if T can be completed to L by adding a 1-manifold with 2n boundary components exterior to M. The link L is called a closure of T. We focus on the case of (S_1 x D_2, 2)-tangles, also called genus-1 tangles, and consider the following question: given a genus-1 tangle G and a link L, how can we tell if L is a closure of …
Invariants Of Legendrian Products, Peter Lambert-Cole
Invariants Of Legendrian Products, Peter Lambert-Cole
LSU Doctoral Dissertations
This thesis investigates a construction in contact topology of Legendrian submanifolds called the Legendrian product. We investigate and compute invariants for these Legendrian submanifolds, including the Thurston-Bennequin invariant and Maslov class; Legendrian contact homology for the product of two Legendrian knots; and generating family homology.
The Kauffman Bracket Skein Module Of The Quaternionic Manifold, John Michael Harris
The Kauffman Bracket Skein Module Of The Quaternionic Manifold, John Michael Harris
LSU Doctoral Dissertations
In this work, we study the structure of the Kauffman bracket skein module of the quaternionic manifold over the field of rational functions. We begin with a brief survey of manifolds whose Kauffman bracket skein modules are known, and proceed in Chapter 2 by recalling the facts from Temperley-Lieb recoupling theory that we use in the proofs. In Chapter 3, using recoupling theory and with Mathematica's assistance, we index an infinite presentation of the skein module, and conjecture that it is five-dimensional. In Chapter 4, using a new set of relations, we prove that the skein module is indeed spanned …