Floer Homology Groups in Yang-Mills Theory

Fields-medal winner Donaldson reviews current work, including his own, on the theory of Floer.

S. K. Donaldson (Author), M. Furuta (Assisted by), D. Kotschick (Assisted by)

9780521808033, Cambridge University Press

Hardback, published 10 January 2002

246 pages
22.6 x 16.9 x 1.8 cm, 0.532 kg

'… gives a nice account of the theory of an interesting topic in contemporary geometry and topology. It can be strongly recommended …'. EMS Newsletter

The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer's construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject.

1. Introduction
2. Basic material
3. Linear analysis
4. Gauge theory and tubular ends
5. The Floer homology groups
6. Floer homology and 4-manifold invariants
7. Reducible connections and cup products
8. Further directions.

Subject Areas: Applied mathematics [PBW], Topology [PBP], Geometry [PBM]