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A real-analytic nonpolynomially convex isotropic torus with no attached discs

  • Purvi Gupta,
    Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada
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Abstract

We show by means of an example in $\mathbb C^3$ that Gromov's theorem on the presence of attached holomorphic discs for compact Lagrangian manifolds is not true in the subcritical real-analytic case, even in the absence of an obvious obstruction, i.e, polynomial convexity.
Keywords: polynomial hull, isotropic submanifold, holomorphic disc polynomial hull, isotropic submanifold, holomorphic disc
MSC Classifications: 32V40, 32E20, 53D12 show english descriptions Real submanifolds in complex manifolds
Polynomial convexity
Lagrangian submanifolds; Maslov index
32V40 - Real submanifolds in complex manifolds
32E20 - Polynomial convexity
53D12 - Lagrangian submanifolds; Maslov index
 

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