Browsing by Author "Seger, Sarah"

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    Lower Order Solvability, Seifert Forms, and Blanchfield Forms of Links
    (2019-04-18) Seger, Sarah; Harvey, Shelly
    We define and study specific generalizations of Seifert forms and Blanchfield forms to links and study their relationships with lower order solvability and with each other. We define Seifert Z-surfaces for links with pairwise linking numbers zero and prove that if a link is 0.5-solvable then every Seifert Z-surface has a metabolizer. We use this result to determine that Arf invariants and Milnor's invariants are not sufficient to classify 0.5-solvable links. We define nonsingular localized Blanchfield forms for links with pairwise linking numbers zero and build on work of Cochran-Orr-Teichner and Cochran-Harvey-Leidy to show that 1-solvability implies each of these Blanchfield forms are hyperbolic. We also define Blanchfield forms on the infinite cyclic covers of the exterior of a link with pairwise linking numbers zero and build on work of Friedl-Powell to prove that in a special case, a Seifert Z-surface having a metabolizer implies the Blanchfield form is hyperbolic. There are well known definitions of boundary Seifert surfaces and multivariable Blanchfield forms for boundary links. We define a boundary metabolizer for a boundary Seifert surface, which is more restrictive than the usual definition of a metabolizer, and prove that the existence of a boundary metabolizer implies both 0.5-solvability and that the multivariable Blanchfield form is hyperbolic.