J-Holomorphic Curves and Quantum Cohomology
Dusa McDuff, Dietmar Salamon, "J-Holomorphic Curves and Quantum Cohomology"
1994 | pages: 220 | ISBN: 0821803328 | PDF | 7,3 mb
1994 | pages: 220 | ISBN: 0821803328 | PDF | 7,3 mb
McDuff and Salamon give complete proofs of Gromov's compactness theorem for spheres and of the existence of the Gromov-Witten invariants. The second half of the book focuses on the definition of quantum cohomology. The authors establish that this multiplication exists, and give a new proof of the Ruan-Tian result that is associative on appropriate manifolds. They then describe the Givental-Kim calculation of the quantum cohomology of flag manifolds, leading to quantum Chern classes and Witten's calculation for Grassmannians, which relates to the Verlinde algebra. The Dubrovin connection, Gromov-Witten potential on quantum cohomology, and curve counting formulas are also discussed. The book closes with an outline of connections to Floer theory.
My Links