The (n)-Solvable Filtration of the Link Concordance Group and Milnor's mu-Invariaants

Date
2011
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Abstract

We 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.

Description
Degree
Doctor of Philosophy
Type
Thesis
Keywords
Pure sciences, Knot theory, Link concordance, Solvable filtration, String links, Mathematics
Citation

Otto, Carolyn Ann. "The (n)-Solvable Filtration of the Link Concordance Group and Milnor's mu-Invariaants." (2011) Diss., Rice University. https://hdl.handle.net/1911/70379.

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