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Award ID contains: 1904074

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  1. ; (, Geometry & Topology)
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  2. ; (, Compositio Mathematica)
    We define a suitably tame class of singular symplectic curves in 4-manifolds, namely those whose singularities are modeled on complex curve singularities. We study the corresponding symplectic isotopy problem, with a focus on rational curves with irreducible singularities (rational cuspidal curves) in the complex projective plane. We prove that every such curve is isotopic to a complex curve in degrees up to five, and for curves with one singularity whose link is a torus knot. Classification results of symplectic isotopy classes rely on pseudo-holomorphic curves together with a symplectic version of birational geometry of log pairs and techniques from four-dimensional topology. 
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  3. ; ; (, Journal of Topology)
  4. ; ; ; ; ; (, Association for Women in Mathematics series)
    Acu, Bahar; Cannizzo, Catherine; McDuff, Dusa; Myer, Ziva; Traynor, Lisa; Pan, Yu (Ed.)
    In this article, we provide an introduction to an algorithm for constructing Weinstein handlebodies for complements of certain smoothed toric divisors using explicit coordinates and a simple example. This article also serves to welcome newcomers to Weinstein handlebody diagrams and Weinstein Kirby calculus. Finally, we include several complicated examples at the end of the article to showcase the algorithm and the types of Weinstein Kirby diagrams it produces. 
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