Microlocal Theory of Sheaves and Tamarkin’s Non Displaceability Theorem

DOI10.1007/978-3-319-06514-4_3zbMath1319.32006arXiv1106.1576OpenAlexW2963236155MaRDI QIDQ5265226

Pierre Schapira, Stéphane Guillermou

Publication date: 23 July 2015

Published in: Lecture Notes of the Unione Matematica Italiana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.1576

zbMATH Keywords

symplectic geometrycategory of torsion objectsmircrolocal theory of sheaves

Mathematics Subject Classification ID

Sheaves of differential operators and their modules, (D)-modules (32C38) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27)

Related Items (21)

Sheaves and \(\mathcal{D}\)-modules on Lorentzian manifolds ⋮ A microlocal characterization of Lipschitz continuity ⋮ Riemann-Hilbert correspondence for holonomic \(\mathcal{D}\)-modules ⋮ Ephemeral persistence modules and distance comparison ⋮ Topological computation of some Stokes phenomena on the affine line ⋮ Enhanced perversities ⋮ Enhanced nearby and vanishing cycles in dimension one and Fourier transform ⋮ Sheaf quantization of Hamiltonian isotopies and applications to nondisplaceability problems ⋮ Sheaf quantization and intersection of rational Lagrangian immersions ⋮ Microlocal theory of Legendrian links and cluster algebras ⋮ The \(\gamma\)-support as a micro-support ⋮ Wrapped sheaves ⋮ Irregular holonomic kernels and Laplace transform ⋮ The non-equivariant coherent-constructible correspondence and a conjecture of King ⋮ Legendrian weaves: \(N\)-graph calculus, flag moduli and applications ⋮ On a topological counterpart of regularization for holonomic \(\mathscr{D}\)-modules ⋮ The nonequivariant coherent-constructible correspondence for toric stacks ⋮ Enhanced specialization and microlocalization ⋮ A microlocal approach to the enhanced Fourier-Sato transform in dimension one ⋮ Compact exact Lagrangian intersections in cotangent bundles via sheaf quantization ⋮ Persistent homology and microlocal sheaf theory

Cites Work

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• Sheaf quantization of Hamiltonian isotopies and applications to nondisplaceability problems
• Microlocal branes are constructible sheaves
• Microlocal condition for non-displaceability
• Exact Lagrangian submanifolds in simply-connected cotangent bundles
• Constructible sheaves and the Fukaya category
• Categories and Sheaves
• Floer homology of open subsets and a relative version of Arnold's conjecture

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