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

• Other Authors: Harvey, Shelly
• Format: Others
• Language: English
• Published: 2013
• Subjects: Pure sciences; Knot theory; Link concordance; Solvable filtration; String links; Mathematics
• Online Access: http://hdl.handle.net/1911/70379

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.