Rational Witt Classes of 4-Stranded Pretzel Knots

Abstract

The rational Witt classes of knots are invariants related to knot concordance. Although they are somewhat weaker than other concordance invariants, for example, the algebraic concordance classes, they are much easier to compute. The goal of this thesis is to obstruct sliceness of 4-stranded pretzel knots by obtaining specific numerical restrictions on the parameters of the knot. We begin by building the theory of bilinear forms over arbitrary fields and construct our main tool, the rational Witt ring. Some examples are presented and we address the specific case of 4-stranded pretzel knots, which exhibit interesting phenomena in the restrictions of the parameters to ensure triviality of their Witt class.