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.
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.
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.
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.
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