Floer Homology Groups in Yang-Mills Theory

S.K. Donaldson

236 pages, parution le 15/03/2002

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Résumé

The concept of Floer homology has been one of the most striking developments in differential geometry over the past 20 years. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas have 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.

Contents

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.

Bibliography
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	S.K. Donaldson
Parution	15/03/2002
Nb. de pages	236
Format	15,5 x 23,5
Couverture	Broché
Poids	474g
Intérieur	Noir et Blanc
EAN13	9780521808033
ISBN13	978-0-521-80803-3