Knot concordance and Blanchfield duality

Shelly Harvey, Rice University

In 1997, Cochran, Orr and Teichner defined a filtration of the
classical knot concordance group, {Fn}, called the (n)-solvable
filtration.  This filtration is geometrically significant because it
measures the successive failure of the Whitney trick for 2-disks in
4-manifolds.  It was shown by Cochran and Teichner that each of the
abelian groups Fn/Fn+1 has rank at least 1.  We show for each n,
that Fn/Fn+1 has infinite rank.  This was only previously known to
be true when n=0,1,2.  We also resolve a long standing question as to
whether certain natural families of knots considered by Casson,
Gordon, Gilmer and others contain slice knots.  This is joint work
with Tim Cochran (Rice University) and Constance Leidy (Wesleyan
University).