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Award ID contains: 2204214

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  1. ; (, Michigan Mathematical Journal)
    Free, publicly-accessible full text available January 1, 2026
  2. (, Journal of the European Mathematical Society)
    Works of Hosokawa–Kawauchi (1979) and Baykur–Sunukjian (2016) show 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 4-ball which have arbitrarily large stabilization distance, giving the first examples of exotic behavior in the 4-ball for which “one is not enough”. 
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    Free, publicly-accessible full text available November 22, 2025
  3. ; ; (, International Press)
    Gross, David; Yao, Andrew Chi-Chih; Yau, Shing-Tung (Ed.)
    Accepted Manuscript Full Text Available
  4. (, Fundamenta Mathematicae)
    We show that there is an associative algebra $$\tilde{H}_n$$ such that, over a base ring R of characteristic 2, Khovanov's arc algebra $$H_n$$ is isomorphic to the algebra $$\tilde{H}_n[x]/(x^2)$$. We also show a similar result for bimodules associated to planar tangles and prove that there is no such isomorphism over the integers. 
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