Harvey, Shelly2013-03-082013-03-082011Otto, Carolyn Ann. "The (n)-Solvable Filtration of the Link Concordance Group and Milnor's mu-Invariaants." (2011) Diss., Rice University. <a href="https://hdl.handle.net/1911/70379">https://hdl.handle.net/1911/70379</a>.https://hdl.handle.net/1911/70379We establish several new results about the ( n )-solvable filtration, [Special characters omitted.] , of the string link concordance group [Special characters omitted.] . We first establish a relationship between ( n )-solvability of a link and its Milnor's μ-invariants. We study the effects of the Bing doubling operator on ( n )-solvability. Using this results, we show that the "other half" of the filtration, namely [Special characters omitted.] , is nontrivial and contains an infinite cyclic subgroup for links with sufficiently many components. We will also show that links modulo (1)-solvability is a nonabelian group. Lastly, we prove that the Grope filtration, [Special characters omitted.] of [Special characters omitted.] is not the same as the ( n )-solvable filtration.69 p.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Pure sciencesKnot theoryLink concordanceSolvable filtrationString linksMathematicsThesisOttoCTHESIS MATH. 2011 OTTO