We revisit the axioms of Scarsini, defining bivariate concordance measures for a pair continuous random variables (X,Y); such can be understood as functions copula C associated with (X,Y). Two constructions, investigated in works Edwards, Mikusiński, Taylor, and Fuchs, are generalized, yielding, particular, examples higher than degree-two polynomial-type measures, along non-polynomial-type prov...

We define two concordance invariants of knots using framed instanton homology. These $\nu^\sharp$ and $\tau^\sharp$ provide bounds on slice genus maximum self-linking number, the latter is a homomorphism which agrees in all known cases with $\tau$ invariant Heegaard Floer use to compute homology nonzero rational Dehn surgeries on: 20 35 nontrivial prime through 8 crossings, infinite families tw...