Linear Independence of Knots Arising from Iterated Infection Without the Use of Tristram Levine Signatures

Details Linear Independence of Knots Arising from Iterated Infection Without the Use of Tristram Levine Signatures Linear Independence of Knots Arising from Iterated Infection Without the Use of Tristram Levine Signatures

2011-08-23

arxiv.org/abs/1108.4477v2

Mathematics

Geometric Topology

28 pages, 2 figures version 2: Corrected some citation and typographical errors

Scientific paper

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 \rho^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.

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