1549055384-Symplectic_Geometry_and_Topology__Eliashberg_

Lecture 3. QH*(G/B) and Quantum Toda Lattices The following proposition has been so far the most efficient tool for computing re ...

248 A. GIVENTAL, A TUTORIAL ON QUANTUM COHOMOLOGY (on the level of simple complex Lie algebras the classical series Br and Cr ar ...

LECTURE 3. QH*(G/B) AND QUANTUM TODA LATTICES 249 ( d) Using 1-st Chern classes of line bundles identify t he lattice of weights ...

250 A. GIVENTAL, A TUTORIAL ON QUANTUM COHOMOLOGY Corollary 3.6. Let D(nq gq, q, n) be a polynomial differential operator commut ...

LECTURE 3. QH*(G/B) AND QUANTUM TODA LATTICES 251 In fact the bi-invariant laplacian on the group gives rise to the hamiltonian ...

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Lecture 4. Singularity Theory In quantum cohomology theory we have encountered a linear pencil of fiat connections (4) on a triv ...

254 A. GIVENTAL, A TUTORIAL ON QUANTUM COHOMOLOGY (c) Show that Lis given by the characteristic equation det(A^1 - LPidti) = 0 ( ...

LECTURE 4. SINGULARITY THEORY 255 Tt B. The pull-back of the action 1-form L_pidti to the critical set by the map y ___, p(y) is ...

256 A. GIVENTAL, A TUTORIAL ON QUANTUM COHOMOLOGY Exercise. The Gaussian integral J~ 00 exp(-ay^2 /li)dy with positive a and Ii ...

LECTURE 4. SINGULARITY THEORY 257 manifolds. Compare these results with properties of complex "oscillating" integrals with const ...

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Lecture 5. Toda Lattices and the Mirror Conjecture The example of the mirror partner for CP^1 can b e generalized to the manifol ...

260 A. GIVENTAL, A TUTORIAL ON QUANTUM COHOMOLOGY Tv corresponding to the vertices v of the lattice: Y< = exp(Tv+ -Tv_) where ...

LECTURE 5. TODA LATTICES AND THE MIRROR CONJECTURE 261 Since Vis invertible, the matrix UV is similar to B =VU. We find: V1 - U1 ...

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Bibliography V. I. Arnold. Sur un propriete topologique des applications canoniques de la mechanique classique. C. R. Acad. Sci ...

264 A. GIVENTAL, A TUTORIAL ON QUANTUM COHOMOLOGY 16. A. Givental & B. Kim. Quantum cohomology of flag manifolds and Toda la ...

Euler Characteristics and Lagrangian Intersections Mikhail Grinberg and Robert MacPherson ...

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