Geometry of Low-Dimensional Manifolds

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 during the 1990s, 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.

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.

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Geometry of Low-Dimensional Manifolds

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