Geometry of Low-Dimensional Manifolds: Volume 1, Gauge Theory and Algebraic Surfaces

This volume is based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds.

S. K. Donaldson (Edited by), C. B. Thomas (Edited by)

9780521399784, Cambridge University Press

Paperback, published 24 January 1991

276 pages
22.8 x 15.3 x 1.6 cm, 0.424 kg

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.

Contributors
Names of Participants
Introduction
Acknowledgments
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 Ronald Fintushel and Ronald J. Stern
9. On the Floer homology of Seifert fibered homology 3-spheres Christian Okonek
10. Za-invariant SU(2) instantons over the four-sphere Mikio Furuta
Part III. Differential Geometry and Mathematical Physics
11. 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.

Subject Areas: Algebraic geometry [PBMW]