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Manifestations Of Symmetry In Polynomial Link Invariants, Kyle Istvan
Manifestations Of Symmetry In Polynomial Link Invariants, Kyle Istvan
LSU Doctoral Dissertations
The use and detection of symmetry is ubiquitous throughout modern mathematics. In the realm of low-dimensional topology, symmetry plays an increasingly significant role due to the fact that many of the modern invariants being developed are computationally expensive to calculate. If information is known about the symmetries of a link, this can be incorporated to greatly reduce the computation time. This manuscript will consider graphical techniques that are amenable to such methods. First, we discuss an obstruction to links being periodic, developed jointly with Dr. Khaled Qazaqzeh at Kuwait University, using a model developed by Caprau and Tipton. We will …
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.