Description
Book SynopsisThis 2007 book provides a comprehensive treatment of Floer homology, based on the Seiberg–Witten equations. Suitable for beginning graduate students and researchers in the field, this book provides a full discussion of a central part of the study of the topology of manifolds.
Trade Review'… there are mathematics books that are classics; these are books that tell a particular story in the right way. As such, they will never go out of date and never be bettered. Kronheimer and Mrowka's book is almost surely such a book. If you want to learn about Floer homology in the Seiberg–Witten context, you will do no better than to read Kronheimer and Mrowka's masterpiece Monopoles and Three-Manifolds.' Clifford Henry Taubes, Bulletin of the American Mathematical Society
'This long-awaited book is a complete and detailed exposition of the Floer theory for Seiberg-Witten invariants. It is very nicely written and contains all proofs of results. This makes the book an essential tool for both researchers and students working in this area of mathematics.' Mathematical Reviews
'This book is the definitive bible for anyone wanting to learn the full story of the various Seiberg-Witten Floer homology theories … There are mathematics books that are classics. As such, they will never go out of date and never be improved. The present masterpiece is almost surely such a book.' Alexander Felshtyn, Zentralblatt MATH
Table of ContentsPreface; 1. Outlines; 2. The Seiberg–Witten equations and compactness; 3. Hilbert manifolds and perturbations; 4. Moduli spaces and transversality; 5. Compactness and gluing; 6. Floer homology; 7. Cobordisms and invariance; 8. Non-exact perturbations; 9. Calculations; 10. Further developments; References; Glossary of notation; Index.
