Von Neumann Rho Invariants as Obstructions to Torsion in the Topological Knot Concordance Group

Details Von Neumann Rho Invariants as Obstructions to Torsion in the Topological Knot Concordance Group Von Neumann Rho Invariants as Obstructions to Torsion in the Topological Knot Concordance Group

2010-10-24

arxiv.org/abs/1010.5020v2

Mathematics

Geometric Topology

33 pages, 14 figures. Clarifications made to theorem statements and definitions, Lemma 5.9 strengthened as needed, A citation

Scientific paper

We discuss an infinite class of metabelian Von Neumann rho-invariants. Each one is a homomorphism from the monoid of knots to the real line. In general they are not well defined on the concordance group. Nonetheless, we show that they pass to well defined homomorphisms from the subgroup of the concordance group generated by anisotropic knots. Thus, the computation of even one of these invariants can be used to conclude that a knot is of infinite order. We introduce a method to give a computable bound on these invariants. Finally we compute this bound to get a new and explicit infinite set of twist knots which is linearly independent in the concordance group and whose every member is of algebraic order 2 .

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