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: Names of Participants
Part I. Four-Manifolds and Algebraic Surfaces:
1. Yang-Mills invariants of four-manifolds S.
2. On the topology of algebraic surfaces Robert
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
5. Flat algebraic manifolds F. A. E. Johnson
Part II. Floer's Instanton Homology Groups:
Instanton homology, surgery and knots Andreas
6. Instanton homology Andreas Floer, notes by
7. Invariants for homology 3-spheres Ronald
Fintushel and Ronald J. Stern
8. On the Floer homology of Seifert fibered
homology 3-spheres Christian Okonek
9. 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
10. Representations of braid groups and
operators coupled to monopoles Ralph E. Cohen
and John D. S. Jones
11. Extremal immersions and the extended frame
bundle D. H. Hartley and R. W. Tucker
12. Minimal surfaces in quaternionic symmetric
spaces F. E. Burstall
13. Three-dimensional Einstein-Weyl geometry K.
14. Harmonic morphisms, conformal foliations
and Seifert fibre spaces John C. Wood. Volume
II: Names of Participants
Part I. Symplectic Geometry: 1. Introduction
2. Rational and ruled symplectic 4-manifolds
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.
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.
14. Pin structures on low-dimensional manifolds
R. C. Kirby and L. R. Taylor.