Fukaya Categories and Picard-Lefschetz TheoryEuropean Mathematical Society, 2008 - 326 Seiten The central objects in the book are Lagrangian submanifolds and their invariants, such as Floer homology and its multiplicative structures, which together constitute the Fukaya category. The relevant aspects of pseudo-holomorphic curve theory are covered in some detail, and there is also a self-contained account of the necessary homological algebra. Generally, the emphasis is on simplicity rather than generality. The last part discusses applications to Lefschetz fibrations and contains many previously unpublished results. The book will be of interest to graduate students and researchers in symplectic geometry and mirror symmetry. |
Häufige Begriffe und Wortgruppen
A-category a₁ algebraic apply argument associated assume base boundary brane bundle canonical carries choice choose cohomology collection compatible complex composition condition connected consider consisting construction corresponding critical datum defined definition deformation denote determinant direct disc discussion embedding equal equipped equivariant exact exact Lagrangian fact faithful functor fibre fixed Floer follows Fukaya category function functor given gives gluing grading hence holomorphic homotopy identity induced isomorphism isotopy Lagrangian Lagrangian submanifolds Lefschetz fibration Lemma manifold means morphism namely natural objects operator orientation pair path perturbation data Proof regular relative Remark respect restriction result satisfies sense shows smooth space standard strip-like ends structure Suppose surface symplectic theory triangle trivial twisted unital vanishing vector Y₁ zero