My research aims to answer questions about knots and surfaces in 3- and 4-manifolds using Floer theoretic techniques.
Papers and Preprints
For Exotic Surfaces with Boundary, One Stabilization is Not Enough.
- A result of Baykur-Sunukjian states that homologous surfaces in a 4-manifold become isotopic after a finite number of internal stabilizations, i.e. attaching tubes to the surfaces. A natural question is how many stabilizations are needed before the surfaces become isotopic. In particular, given an exotic pair of surfaces, is a single stabilization always enough to make the pair smoothly isotopic? We answer this question by studying how the stabilization distance between surfaces with boundary changes with respect to satellite operations. Using a range of Floer theoretic techniques, we show that there are exotic disks in the four-ball which have arbitrarily large stabilization distance, giving the first examples of exotic behavior in the four-ball for which "one is not enough"
Ribbon Homology Cobordisms and Link Floer homology.
- We make use of link Floer homology to study cobordisms between links embedded in 4-dimensional ribbon homology cobordisms. Combining results of Daemi--Lidman--Vela-Vick--Wong and Zemke, we show that ribbon homology concordances induce split injections on the minus version of link Floer homology. We also make use of reduced link Floer homology to give restrictions on the number of critical points in ribbon homology concordances.
Papers and Preprints
For Exotic Surfaces with Boundary, One Stabilization is Not Enough.
- A result of Baykur-Sunukjian states that homologous surfaces in a 4-manifold become isotopic after a finite number of internal stabilizations, i.e. attaching tubes to the surfaces. A natural question is how many stabilizations are needed before the surfaces become isotopic. In particular, given an exotic pair of surfaces, is a single stabilization always enough to make the pair smoothly isotopic? We answer this question by studying how the stabilization distance between surfaces with boundary changes with respect to satellite operations. Using a range of Floer theoretic techniques, we show that there are exotic disks in the four-ball which have arbitrarily large stabilization distance, giving the first examples of exotic behavior in the four-ball for which "one is not enough"
Ribbon Homology Cobordisms and Link Floer homology.
- We make use of link Floer homology to study cobordisms between links embedded in 4-dimensional ribbon homology cobordisms. Combining results of Daemi--Lidman--Vela-Vick--Wong and Zemke, we show that ribbon homology concordances induce split injections on the minus version of link Floer homology. We also make use of reduced link Floer homology to give restrictions on the number of critical points in ribbon homology concordances.
- A result of Baykur-Sunukjian states that homologous surfaces in a 4-manifold become isotopic after a finite number of internal stabilizations, i.e. attaching tubes to the surfaces. A natural question is how many stabilizations are needed before the surfaces become isotopic. In particular, given an exotic pair of surfaces, is a single stabilization always enough to make the pair smoothly isotopic? We answer this question by studying how the stabilization distance between surfaces with boundary changes with respect to satellite operations. Using a range of Floer theoretic techniques, we show that there are exotic disks in the four-ball which have arbitrarily large stabilization distance, giving the first examples of exotic behavior in the four-ball for which "one is not enough"