We use moduli spaces of instantons and Chern-Simons invariants of flat connections to prove that the Whitehead doubles of $(2, 2^n − 1)$ torus knots are independent in the smooth knot concordance group; that is, they freely generate a subgroup of infinite rank.
"Instantons, concordance, and Whitehead doubling." J. Differential Geom. 91 (2) 281 - 319, June 2012. https://doi.org/10.4310/jdg/1344430825