Transverse invariants and exotic surfaces in the 4–ball

Using 1–twist rim surgery, we construct infinitely many smoothly embedded, orientable surfaces in the 4–ball bounding a knot in the 3–sphere that are pairwise topologically isotopic, but not ambient diffeomorphic. We distinguish the surfaces using the maps they induce on perturbed link Floer homology. Along the way, we show that the cobordism map induced by an ascending surface in a Weinstein cobordism preserves the transverse invariant in link Floer homology.