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Showing 1 to 9 of 9 for “"Fukaya categories"”.
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Spectral Fukaya Categories for Liouville Manifolds
… wrapped Floer cohomology, and the Donaldson-Fukaya category.
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Quantum Steenrod operations and Fukaya categories
… A∞-category. We show that when applied to the Fukaya category of a nondegenerated closed monotone symplectic manifold, this construction can be identified with the quantum Steenrod operations via Ganatra’s cyclic open-closed maps. A key ingredient in this identification is a new homotopy …
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Distinguishing open symplectic mapping tori via their wrapped Fukaya categories
… precisely, we exploit the dynamics of wrapped Fukaya categories to distinguish an open version of symplectic mapping torus associated to a symplectomorphism from the mapping torus of the identity. As an application, we obtain pairs of diffeomorphic Weinstein domains with the same contact …
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Pseudoholomorphic quilts with figure eight singularity
… into A[infinity],-functors between Fukaya categories. The core of this construction is pseudoholomorphic quilts with figure eight singularity. In the first part, I propose a blueprint for constructing an algebraic object that binds together the Fukaya categories of many different …
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Toric mirror symmetry and GIT windows
… terms and study them in the context of wrapped Fukaya categories and wrapped constructible sheaves. We explain how the mirror image of the Halpern-Leistner-Sam ""magic window"" for quasi-symmetric torus actions computes the category associated to the equivariant semistable skeleton upon stop …
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Symplectic properties of Milnor fibres
… four. This gives examples of Milnor fibres whose Fukaya categories are not generated by vanishing cycles. Also, this allows progress towards mirror symmetry for unimodal singularities, which are one level of complexity up from the simple ones.
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The Fukaya category, exotic forms and exotic autoequivalences
… of associating an A∞-category to M, called its Fukaya category, in helping to understand symplectic properties of M and its Lagrangian submanifolds. One of the principles of this construction is that automorphisms of the symplectic manifold should induce autoequivalences of the derived Fukaya …
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Solitons and dualities in 2+1 dimensions
… the A-twist induces a monoidal structure on the Fukaya categories of a certain, restricted, class of Kähler manifolds. Third, we consider magnetic Skyrmions in ferromagnetic materials. We produce a continuum toy model of fractionalised electrons in three spatial dimensions describing magnetic …
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On a Heegaard Floer theory for tangles
… modules and twisted complexes in the wrapped Fukaya category of the 4-punctured sphere. There are four appendices, some of which might be of independent interest: In the first appendix, we describe a general construction of dg categories which unifies all algebraic structures used in this …