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Abstract
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We discuss an infinite class of metabelian Von Neumann
–invariants.
Each one is a homomorphism from the monoid of knots to
. 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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Keywords
knot concordance, rho-invariants
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57N70
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Publication
Received: 16 February 2011
Revised: 28 September 2011
Accepted: 28 September 2011
Published: 12 April 2012
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