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Sheaf quantization in Weinstein symplectic manifolds
David Nadler,Vivek Shende +1 more
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In this article, a microlocal theory of sheaves is used to associate a category to each Weinstein manifold, and it is shown that exact Lagrangians give objects in the category and that the category is invariant under Weinstein homotopy.Abstract:
Using the microlocal theory of sheaves, we associate a category to each Weinstein manifold. By constructing a microlocal specialization functor, we show that exact Lagrangians give objects in our category, and that the category is invariant under Weinstein homotopy.read more
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Microlocal Morse theory of wrapped Fukaya categories
TL;DR: In this article, the authors generalized the Nadler-Zaslow correspondence to incorporate infinite-dimensional spaces of morphisms at infinity, given on the Floer side by Reeb trajectories (also known as "wrapping") and on the sheaf side by allowing unbounded infinite rank sheaves which are categorically compact.
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Lagrangian Skeleta and Plane Curve Singularities
TL;DR: In this paper, a closed arboreal Lagrangian skeleta associated to links of isolated plane curve singularities is constructed for Weinstein pairs and 4-manifolds associated to max-tb Legendrian representatives of algebraic links.
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Microlocal sheaf categories and the $J$-homomorphism
TL;DR: In this paper, it was shown that the classifying map for the local system of categories factors through the stable Gauss map $L\rightarrow U/O$ and the delooping of the $J$-homomorphism.
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Mirror symmetry for Berglund-H\"ubsch Milnor fibers
TL;DR: The conjecture of Yanki Lekili and Kazushi Ueda on homological mirror symmetry for Milnor fibers of Berglund-Hubsch invertible polynomials was proved in this paper.
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Lagrangian skeleta and plane curve singularities
TL;DR: In this article , the authors construct closed arboreal Lagrangian skeleta associated to links of isolated plane curve singularities. But they do not discuss the contact topological nature of the Fomin-Pylyavskyy-Shustin-Thurston cluster algebra associated to a singularity.
References
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Higher Topos Theory
TL;DR: In this paper, a general introduction to higher category theory using the formalism of "quasicategories" or "weak Kan complexes" is provided, and a few applications to classical topology are included.
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Supersymmetry and Morse theory
TL;DR: In this paper, it was shown that the Morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics Hamiltonian, and some of the implications of modern ideas in mathematics for super-ymmetric theories are discussed.
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TL;DR: A variant of the usual supersymmetric nonlinear sigma model is described in this article, governing maps from a Riemann surface to an arbitrary almost complex manifold, which possesses a fermionic BRST-like symmetry, conserved for arbitrary Σ, and obeying Q 2 = 0.
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Lagrangian Intersection Floer Theory: Anomaly and Obstruction
TL;DR: The Floer cohomology as mentioned in this paper is an algebra associated to a Lagrangian submanifold and is a homotopy equivalence of $A_\infty$ algebras.