#### Volume 25, issue 6 (2021)

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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
##### Abstract

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.

##### Keywords
4-manifolds, exotic surfaces, Heegaard Floer homology
##### Mathematical Subject Classification 2010
Primary: 57R58
Secondary: 57M27, 57R55
##### Publication
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
##### Authors
 András Juhász Mathematical Institute University of Oxford 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