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 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 the first full discussion of a central part of
the study of the topology of manifolds since the mid 1990s.
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