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

ISBN-13: 9780521399784 / Angielski / Miękka / 1991 / 276 str.

S. K. Donaldson; C. B. Thomas; S. K. Donaldson

Opis

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.

Spis treści

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.