Description

This volume is 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 interact (for example: topology, differential and algebraic geometry and mathematical physics). The workshop brought together a number of distinguished figures to give lecture courses and seminars in these subjects; the volume that has resulted is the only expository source for much of the material, and will be essential for all research workers in geometry and mathematical physics. 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.