Lagrangian cobordism and Fukaya categories

DOI10.1007/s00039-014-0305-4zbMath1306.55003arXiv1304.6032OpenAlexW2057312011MaRDI QIDQ484468

Paul Biran, Octavian Cornea

Publication date: 7 January 2015

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.6032

zbMATH Keywords

Floer homologyFukaya categoryLagrangian cobordism

Mathematics Subject Classification ID

(mathrm{O})- and (mathrm{SO})-cobordism (57R75) Bordism and cobordism theories and formal group laws in algebraic topology (55N22) Homological algebra in category theory, derived categories and functors (18G99) Hamiltonian and Lagrangian mechanics (70H99)

Related Items (20)

Categorification of Seidel's representation ⋮ Aspects of functoriality in homological mirror symmetry for toric varieties ⋮ Cone-decompositions of Lagrangian cobordisms in Lefschetz fibrations ⋮ Equivariant split generation and mirror symmetry of special isogenous tori ⋮ Symplectic flexibility and the Grothendieck group of the Fukaya category ⋮ The fundamental group of a rigid Lagrangian cobordism ⋮ Invariants of Lagrangian cobordisms via spectral numbers ⋮ Tropical Lagrangians in toric del-Pezzo surfaces ⋮ On the Fukaya category of a Fano hypersurface in projective space ⋮ Topology of (small) Lagrangian cobordisms ⋮ Lagrangian cobordism. I ⋮ Lagrangian cobordism and tropical curves ⋮ A Lagrangian pictionary ⋮ Khovanov homology from Floer cohomology ⋮ 20 open questions about deformations of compactifiable manifolds ⋮ A stable \(\infty\)-category of Lagrangian cobordisms ⋮ Bounds on the Lagrangian spectral metric in cotangent bundles ⋮ Rational equivalence and Lagrangian tori on K3 surfaces ⋮ Dehn twist exact sequences through Lagrangian cobordism ⋮ Dehn twists and Lagrangian spherical manifolds

Cites Work

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• Homological Lagrangian monodromy
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• Morse theory for Lagrangian intersections
• \(\pi_1\) of symplectic automorphism groups and invertibles in quantum homology rings
• A stable \(\infty\)-category of Lagrangian cobordisms
• Homogeneous coordinate rings and mirror symmetry for toric varieties
• Combinatorial Floer Homology
• A relative Seidel morphism and the Albers map
• Floer cohomology of lagrangian intersections and pseudo‐holomorphic disks I
• Graded lagrangian submanifolds
• Homological Algebra of Mirror Symmetry
• Addendum to “Floer Cohomology of Lagrangian Intersections and Pseudo‐Holomorphic Discs, I”
• Lagrangian cobordism. I
• Fukaya categories of symmetric products and bordered Heegaard-Floer homology
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