Geometry of Low-Dimensional Manifolds: 2: Symplectic Manifolds and Jones-Witten Theory

ISBN-13: 9780521400015 / Angielski / Miękka / 1991 / 260 str.

S. K. Donaldson; C. B. Thomas;Donaldson/Thomas

Opis

These volumes are based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects (topology, differential and algebraic geometry and mathematical physics) interact.

Spis treści

Names of Participants; Introduction; Acknowledgements; Part I. Symplectic Geometry: 1. Introduction; 2. Rational and ruled symplectic 4-manifolds Dusa McDuff; 3. Symplectic capacities H. Hofer; 4. The nonlinear Maslov index A. B. Givental; 5. Filling by holomorphic discs and its applications Yakov Eliashberg; Part II. Jones/Witten Theory: 6. Introduction; 7. New results in Chern-Simons theory Edward Witten, notes by Lisa Jeffrey; 8. Geometric quantization of spaces of connections N. J. Hitchin; 9. Evaluations of the 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2, C) Robion Kirby and Paul Melvin; 10. Representations of braid groups M. F. Atiyah, notes by S. K. Donaldson; Part III. Three-Dimensional Manifolds: 11. Introduction; 12. An introduction to polyhedral metrics of non-positive curvature on 3-manifolds I. R. Aitchison and J. H. Rubinstein; 13. Finite groups of hyperbolic isometries C. B. Thomas; 14. Pin structures on low-dimensional manifolds R. C. Kirby and L. R. Taylor.