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Riemannian manifolds --- Global differential geometry --- Orbifolds --- Three-manifolds (Topology) --- Ricci, flow --- Riemann, Variétés de --- Géométrie différentielle globale --- Orbivariétés --- Variétés topologiques à 3 dimensions --- Ricci, Flot de --- Riemann, Variétés de. --- Géométrie différentielle globale. --- Orbivariétés. --- Variétés topologiques à 3 dimensions. --- Ricci, Flot de. --- Ricci flow.

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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.

Three-manifolds (Topology) --- Homology theory --- Moduli theory --- Variétés topologiques à 3 dimensions --- Homologie --- Variétés topologiques à 4 dimensions --- Variétés topologiques à 3 dimensions --- Variétés topologiques à 4 dimensions --- Homology theory. --- Seiberg-Witten invariants. --- Moduli theory. --- Theory of moduli --- Analytic spaces --- Functions of several complex variables --- Geometry, Algebraic --- Invariants --- Cohomology theory --- Contrahomology theory --- Algebraic topology --- 3-manifolds (Topology) --- Manifolds, Three dimensional (Topology) --- Three-dimensional manifolds (Topology) --- Low-dimensional topology --- Topological manifolds

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Symplectic manifolds. --- Topology. --- Variétés symplectiques --- Topologie --- Varietes symplectiques. --- Topologie. --- 515.16 --- 515.16 Topology of manifolds --- Topology of manifolds --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Manifolds, Symplectic --- Geometry, Differential --- Manifolds (Mathematics) --- Differential geometry --- Differential topology --- Differential geometry. Global analysis --- Chimie topologique --- Algèbre linéaire --- Coloriage --- Géométrie algébrique --- Fonctions invexes --- Analyse ultramétrique --- Anneaux topologiques --- Applications (mathématiques) --- Atiyah-Singer, Théorème d' --- Banach, Espaces de --- Catégories (mathématiques) --- Coincidence, Théorie de la (mathématiques) --- Compactifications --- Dimension, Théorie de la (topologie) --- Dualité, Principe de (mathématiques) --- Dynamique topologique --- Ensembles amas, Théorie des --- Ensembles boréliens --- Espaces de proximité --- Espaces localement compacts --- Espaces métriques --- Espaces topologiques --- Espaces uniformes --- Espaces vectoriels topologiques --- Forme, Théorie de la (topologie) --- Graphes, Théorie des --- Graphes topologiques, Théorie des --- Groupes topologiques --- Hewitt-Nachbin, Espaces de --- Homotopie --- Isométrie (mathématiques) --- Jeux de stratégie (mathématiques) --- Plongements (mathématiques) --- Plongements topologiques --- Point fixe, Théorème du --- Polytopes --- Relèvement (mathématiques) --- Réseaux (mathématiques) --- Rétractes, Théorie des --- Semigroupes topologiques --- Simplexes (mathématiques) --- Topologie algébrique --- Topologie combinatoire --- Topologie de l'espace métrique --- Topologie différentielle --- Topologie ensembliste --- Transformations, Groupes de --- Treillis, Théorie des --- Variétés (mathématiques) --- Variétés topologiques --- Topologie linéaire par morceaux --- Théorie des ensembles --- Géométrie --- Polyèdres --- Géométrie symplectique --- Géométrie différentielle --- mathématiques --- Symplectic manifolds --- Topology --- Varietes symplectiques --- Géometrie différentielle globale --- Géometrie symplectique