Harvey, Shelly2013-09-162013-09-162013-09-162013-09-162013-052013-09-16May 2013Martin, Taylor. "Lower order solvability of links." (2013) Diss., Rice University. <a href="https://hdl.handle.net/1911/71998">https://hdl.handle.net/1911/71998</a>.https://hdl.handle.net/1911/71998The n-solvable filtration of the link concordance group, defined by Cochran, Orr, and Teichner in 2003, is a tool for studying smooth knot and link concordance that yields important results in low-dimensional topology. We focus on the first two stages of the n-solvable filtration, which are the class of 0-solvable links and the class of 0.5-solvable links. We introduce a new equivalence relation on links called 0-solve equivalence and establish both an algebraic and a geometric characterization 0-solve equivalent links. As a result, we completely characterize 0-solvable links and we give a classification of links up to 0-solve equivalence. We relate 0-solvable links to known results about links bounding gropes and Whitney towers in the 4-ball. We then establish a sufficient condition for a link to be 0.5-solvable and show that 0.5-solvable links must have vanishing Sato-Levine invariants.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.Knot theoryLink concordanceN-solvable filtrationBand-pass equivalenceMilnor's invariantsThesis2013-09-16123456789/ETD-2013-05-554