The main goal of this article is to obtain a condition under which an infinite collection
of
satellite knots (with companion a positive torus knot and pattern similar to the
Whitehead link) freely generates a subgroup of infinite rank in the smooth concordance
group. This goal is attained by examining both the instanton moduli space over a
–manifold
with tubular ends and the corresponding Chern–Simons invariant of the adequate
–dimensional portion
of the
–manifold.
More specifically, the result is derived from Furuta’s criterion for the independence of
Seifert fibred homology spheres in the homology cobordism group of oriented homology
–spheres. Indeed, we first
associate to
the corresponding
collection of
–fold covers
of the
–sphere branched
over the elements of
and then introduce definite cobordisms from the aforementioned covers of the satellites
to a number of Seifert fibered homology spheres. This allows us to apply Furuta’s
criterion and thus obtain a condition that guarantees the independence of the family
in the
smooth concordance group.
