Transverse invariants and exotic surfaces in the 4-ball

We explain how to use 1-twist rim surgery to 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 knot Floer homology, together with our result that the cobordism map induced by an ascending surface in a Weinstein cobordism preserves the transverse invariant in knot Floer homology. This is joint work with Maggie Miller and Ian Zemke.

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