Geometry of Low-Dimensional Manifolds
Volume 1, Gauge Theory and Algebraic Surfaces
Herausgeber: Donaldson, S. K.; Thomas, C. B.
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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 a...
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.
Table of contents:
Volume I: Contributors; Names of Participants; Introduction; Acknowledgements; Part I. Four-Manifolds and Algebraic Surfaces; 1. Yang-Mills invariants of four-manifolds S. K. Donaldson; 2. On the topology of algebraic surfaces Robert E. Gompf; 3. The topology of algebraic surfaces with q=pg=0 Dieter Kotschick; 4. On the homeomorphism classification of smooth knotted surfaces in the 4-sphere Matthias Kreck; 5. Flat algebraic manifolds F. A. E. Johnson; Part II: Floer's Instanton Homology Groups; 6. Instanton homology, surgery and knots Andreas Floer; 7. Instanton homology Andreas Floer, notes by Dieter Knotschick; 8. Invariants for homology 3-spheres; 9. Ronald Fintushel and Ronald J. Stern; 10. On the Floer homology of Seifert fibered homology 3-spheres Christian Okonek; 11. Za-invariant SU(2) instantons over the four-sphere Mikio Furuta; Part III. Differential Geometry and Mathematical Physics; Skyrme fields and instantons N. S. Manton; 12. Representations of braid groups and operators coupled to monopoles Ralph E. Cohen and John D. S. Jones; 13. Extremal immersions and the extended frame bundle D. H. Hartley and R. W. Tucker; 14. Minimal surfaces in quaternionic symmetric spaces F. E. Burstall; 15. Three-dimensional Einstein-Weyl geometry K. P. Tod; 16. Harmonic Morphisms, conformal foliations and Seifert fibre spaces John C. Wood. Volume II: Contributors; Names of Participants; Introduction; Acknowledgements; Part I. Symplectic Geometry; Introduction; 1. Rational and ruled symplectic 4-manifolds Dusa McDuff; 2. Symplectic capacities H. Hofer; 3. The nonlinear Maslov index A. B. Givental; 4. Filling by holomorphic discs and its applications Yakov Eliashberg; Part II. Jones/Witten Theory; 5. Introduction; 6. New results in Chern-Simons theory Edward Witten, notes by Lisa Jeffrey; 7. Geometric quantization of spaces of connections N. J. Hitchin; 8. Evaluations of the 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2, C) Robion Kirby and Paul Melvin; 9. Representations of braid groups M. F. Atiyah, notes by S. K. Donaldson; Part III. Three-Dimensional Manifolds; 10. Introduction; 11. An introduction to polyhedral metrics of non-positive curvature on 3-manifolds I. R. Aitchison and J. H. Rubinstein; 12. Finite groups of hyperbolic isometries C. B. Thomas; 13. Pin structures on low-dimensional manifolds R. C. Kirby and L. R. Taylor.
Table of contents:
Volume I: Contributors; Names of Participants; Introduction; Acknowledgements; Part I. Four-Manifolds and Algebraic Surfaces; 1. Yang-Mills invariants of four-manifolds S. K. Donaldson; 2. On the topology of algebraic surfaces Robert E. Gompf; 3. The topology of algebraic surfaces with q=pg=0 Dieter Kotschick; 4. On the homeomorphism classification of smooth knotted surfaces in the 4-sphere Matthias Kreck; 5. Flat algebraic manifolds F. A. E. Johnson; Part II: Floer's Instanton Homology Groups; 6. Instanton homology, surgery and knots Andreas Floer; 7. Instanton homology Andreas Floer, notes by Dieter Knotschick; 8. Invariants for homology 3-spheres; 9. Ronald Fintushel and Ronald J. Stern; 10. On the Floer homology of Seifert fibered homology 3-spheres Christian Okonek; 11. Za-invariant SU(2) instantons over the four-sphere Mikio Furuta; Part III. Differential Geometry and Mathematical Physics; Skyrme fields and instantons N. S. Manton; 12. Representations of braid groups and operators coupled to monopoles Ralph E. Cohen and John D. S. Jones; 13. Extremal immersions and the extended frame bundle D. H. Hartley and R. W. Tucker; 14. Minimal surfaces in quaternionic symmetric spaces F. E. Burstall; 15. Three-dimensional Einstein-Weyl geometry K. P. Tod; 16. Harmonic Morphisms, conformal foliations and Seifert fibre spaces John C. Wood. Volume II: Contributors; Names of Participants; Introduction; Acknowledgements; Part I. Symplectic Geometry; Introduction; 1. Rational and ruled symplectic 4-manifolds Dusa McDuff; 2. Symplectic capacities H. Hofer; 3. The nonlinear Maslov index A. B. Givental; 4. Filling by holomorphic discs and its applications Yakov Eliashberg; Part II. Jones/Witten Theory; 5. Introduction; 6. New results in Chern-Simons theory Edward Witten, notes by Lisa Jeffrey; 7. Geometric quantization of spaces of connections N. J. Hitchin; 8. Evaluations of the 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2, C) Robion Kirby and Paul Melvin; 9. Representations of braid groups M. F. Atiyah, notes by S. K. Donaldson; Part III. Three-Dimensional Manifolds; 10. Introduction; 11. An introduction to polyhedral metrics of non-positive curvature on 3-manifolds I. R. Aitchison and J. H. Rubinstein; 12. Finite groups of hyperbolic isometries C. B. Thomas; 13. Pin structures on low-dimensional manifolds R. C. Kirby and L. R. Taylor.