TY - BOOK ID - 5549606 TI - Monopoles and three-manifolds AU - Kronheimer, P. B AU - Mrowka, Tomasz PY - 2007 VL - 10 SN - 9780521880220 052188022X 9780511543111 9780521184762 9780511379093 0511379099 9780511376399 0511376391 0511543115 0521184762 1107184266 9781107184268 1281243620 9781281243621 9786611243623 6611243623 0511378203 9780511378201 0511377339 9780511377334 0511374879 9780511374876 PB - Cambridge Cambridge University Press DB - UniCat KW - Three-manifolds (Topology) KW - Homology theory KW - Moduli theory KW - Variétés topologiques à 3 dimensions KW - Homologie KW - Variétés topologiques à 4 dimensions KW - Variétés topologiques à 3 dimensions KW - Variétés topologiques à 4 dimensions KW - Homology theory. KW - Seiberg-Witten invariants. KW - Moduli theory. KW - Theory of moduli KW - Analytic spaces KW - Functions of several complex variables KW - Geometry, Algebraic KW - Invariants KW - Cohomology theory KW - Contrahomology theory KW - Algebraic topology KW - 3-manifolds (Topology) KW - Manifolds, Three dimensional (Topology) KW - Three-dimensional manifolds (Topology) KW - Low-dimensional topology KW - Topological manifolds UR - https://www.unicat.be/uniCat?func=search&query=sysid:5549606 AB - 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. ER -