Let be any integer-valued additive knot invariant that bounds the smooth 4–genus of a knot , , and determines the 4–ball genus of positive torus knots, . Either of the knot concordance invariants of Ozsváth-Szabó or Rasmussen, suitably normalized, have these properties. Let denote the positive or negative –twisted double of . We prove that if , then . It is also shown that for all and for all , where denotes the Thurston-Bennequin number.
A realization result is also presented: for any Seifert matrix and integer , , there is a knot with Seifert form and .
"Ozsváth–Szabó and Rasmussen invariants of doubled knots." Algebr. Geom. Topol. 6 (2) 651 - 657, 2006. https://doi.org/10.2140/agt.2006.6.651