TY  - BOOK
AU  - Kronheimer,P.B.
AU  - Mrowka,Tomasz
TI  - Monopoles and three-manifolds
T2  - New mathematical monographs
SN  - 9780511543111 (ebook)
AV  - QA613.2 .K76 2007
U1  - 514/.3 22
PY  - 2007///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Three-manifolds (Topology)
KW  - Homology theory
KW  - Seiberg-Witten invariants
KW  - Moduli theory
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); Outlines -- The Seiberg-Witten equations and compactness -- Hilbert manifolds and perturbations -- Moduli spaces and transversality -- Compactness and gluing -- Floer homology -- Cobordisms and invariance -- Non-exact perturbations -- Calculations
N2  - Originating with Andreas Floer in the 1980s, Floer homology has proved to be an effective tool in tackling many important problems in three- and four-dimensional geometry and topology. This 2007 book provides a comprehensive treatment of Floer homology, based on the Seiberg-Witten monopole equations. After first providing an overview of the results, the authors develop the analytic properties of the Seiberg-Witten equations, assuming only a basic grounding in differential geometry and analysis. The Floer groups of a general three-manifold are then defined and their properties studied in detail. Two final chapters are devoted to the calculation of Floer groups and to applications of the theory in topology. Suitable for beginning graduate students and researchers, this book provides a full discussion of a central part of the study of the topology of manifolds
UR  - https://doi.org/10.1017/CBO9780511543111
ER  -