1549055384-Symplectic_Geometry_and_Topology__Eliashberg_

Bibliography l. M.F. Atiyah, V .K. Patodi and l.M. Singer, Spectral asymmetry and Riemann- ian geometry, Math. Proc. Camb. Phil. ...

228 D. SALAMON, FLOER HOMOLOGY A. Givental, Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror co ...

BIBLIOGRAPHY 229 J.W. Robbin and D.A. Salamon, The spectral fl.ow and the Maslov index, Bulletin of the LMS 27 (1995), 1-33. Y. ...

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A Tutorial on Quantum Cohomology Alexander Givental ...

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!AS/Park City Mathematics Series Volume 7, 1999 A Tutorial on Quantum Cohomology Alexander Givental Introduction Let (M, f, G) b ...

234 A. GIVENTAL, A TUTORIAL ON QUANTUM COHOMOLOGY are involved into the construction of Floer homology theory in the context of ...

INTRODUCTION 235 by E. Witten and motivated by ideas of 1 + 1-dimensional conformal field theory. Witten showed that various enu ...

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LECTURE 1 Moduli Spaces of Stable Maps 1. Example: Quantum cohomology of complex projective spaces In quantum cohomology theory ...

238 A. GIVENTAL, A TUTORIAL ON QUANTUM COHOMOLOGY Exercise. Check that higher degree spheres do not contribute to the structural ...

LECTURE 1. MODULI SPACES OF STABLE MAPS 239 curves can degenerate to reducible ones but in the limit the genus and degree are co ...

240 A. GIVENTAL, A TUTORIAL ON QUANTUM COHOMOLOGY on (E, E) a map equivalent to f. Thus the diagram defined by the projection ft ...

Lecture 2. Gromov-Witten Invariants Structural constants of the quantum cup-product on H* (X) are defined by (aob,c) := L:qt' .. ...

242 A. GIVENTAL, A TUTORIAL ON QUANTUM COHOMOLOGY Notice that the configuration of points mapped to the cycles is not specified, ...

LECTURE 2. GROMOV-WITTEN INVARIANTS 243 combination of the structural constants L (a1 o a2, ¢ 0 )r/"^13 (¢13, a 3 o a 4 ) , o:,/ ...

. 244 A. GIVENTAL, A TUTORIAL ON QUANTUM COHOMOLOGY Prove the divisor equation by computing the push-forward (ft2)* ev2(Pi) from ...

LECTURE 2. GROMOV-WITTEN INVARIANTS 245 and the 2-nd marked points, and the 3-rd marked point is located on the 2-nd <CP^1. A ...

246 A. GIVENTAL, A TUTORIAL ON QUANTUM COHOMOLOGY Exercise. Define the genus 0 potential of X as the following formal function o ...