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Transverse invariants and exotic surfaces in the $4$–ball

András Juhász, Maggie Miller and Ian Zemke

Geometry & Topology 25 (2021) 2963–3012

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.

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4-manifolds, exotic surfaces, Heegaard Floer homology
Mathematical Subject Classification 2010
Primary: 57R58
Secondary: 57M27, 57R55
Received: 1 February 2020
Revised: 18 September 2020
Accepted: 13 November 2020
Published: 30 November 2021
Proposed: András I Stipsicz
Seconded: Peter Ozsváth, Paul Seidel
András Juhász
Mathematical Institute
University of Oxford
United Kingdom
Maggie Miller
Department of Mathematics
Princeton University
Princeton, NJ
United States
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
Ian Zemke
Department of Mathematics
Princeton University
Princeton, NJ
United States