  We consider the FK-Ising model in two dimensions at criticality. We obtain
bounds on crossing probabilities of arbitrary topological rectangles, uniform
with respect to the boundary conditions, generalizing results of [DCHN11] and
[CS12]. Our result relies on new discrete complex analysis techniques,
introduced in [Che12]. We detail some applications, in particular the
computation of so-called universal exponents, the proof of
quasi-multiplicativity properties of arm probabilities, and bounds on crossing
probabilities for the classical Ising model.
