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

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.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Natural Sciences

Grantor

Rice University

Year dc:date.issued

2011

Author dc:creator

• Otto, Carolyn Ann

Advisor dc:contributor.advisor

• Harvey, Shelly

• Pure sciences
• Knot theory
• Link concordance
• Solvable filtration
• String links
• Mathematics

Statement dc:rights

• Copyright 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.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/70379

OAI identifier oai:identifier

oai:repository.rice.edu:1911/70379