Linear Independence of Knots Arising from Iterated Infection Without the Use of Tristram Levine Signatures
arXiv:1108.4477
Abstract
We give an explicit construction of linearly independent families of knots arbitrarily deep in the (n)-solvable filtration of the knot concordance group using the ρ^1-invariant. A difference between previous constructions of infinite rank subgroups in the concordance group and ours is that the deepest infecting knots in the construction we present are allowed to have vanishing Tristram-Levine signatures.
28 pages, 2 figures version 2: Corrected some citation and typographical errors