This paper highlights the importance of string link concordance in
the understanding of knot concordance in general. The results of this
paper show that there are infinitely many nontrivial knots in the groups
of
–solvable knots
modulo –solvable
knots, for greater
than or equal to ,
which are not concordant to any knot that is obtained by two or more
iterated infections of an Arf invariant zero knot by knots. This latter
class accounts for nearly all previously known examples of knots in
,
greater than
or equal to .
In this paper we will generalize the concept of when a rational Laurent
polynomial is strongly coprime to another, first introduced by Cochran, Harvey and
Leidy, to include multivariable polynomials. We also prove the existence of
multivariable polynomials which are strongly coprime to all single variable Laurent
polynomials. From this definition of coprimality we define the derived series localized
at
for a given sequence of multivariable polynomials
. From such series we obtain
refinements of the –solvable
filtration. The operation of infection by a string link is then used to demonstrate that for
particular ,
certain quotients of successive terms of these refined filtrations have infinite
rank.
