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Valuation theory --- Ordered fields --- K-theory --- Algebraic number theory --- Topological fields --- Algebraic topology --- Homology theory

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Frobenius algebras --- Topological fields --- Quantum field theory --- Group theory --- Algèbres de Frobenius --- Corps topologiques --- Théorie quantique des champs

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This book addresses a gap in the model-theoretic understanding of valued fields that had limited the interactions of model theory with geometry. It contains significant developments in both pure and applied model theory. Part I of the book is a study of stably dominated types. These form a subset of the type space of a theory that behaves in many ways like the space of types in a stable theory. This part begins with an introduction to the key ideas of stability theory for stably dominated types. Part II continues with an outline of some classical results in the model theory of valued fields and explores the application of stable domination to algebraically closed valued fields. The research presented here is made accessible to the general model theorist by the inclusion of the introductory sections of each part.

Model theory --- Valued fields --- Domination (Graph theory) --- Model theory. --- Valued fields. --- Graph theory --- Fields, Valued --- Topological fields --- Logic, Symbolic and mathematical

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This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work.

Frobenius algebras. --- Topological fields. --- Quantum field theory. --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Algebraic fields --- Algebras, Frobenius --- Associative algebras

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Topological fields. --- Generalized spaces. --- Topology. --- Corps topologiques. --- Espaces généralisés. --- Topologie. --- Corps topologiques --- Espaces généralisés --- Topological fields --- Generalized spaces --- Topology --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Calculus of tensors --- Geometry, Differential --- Geometry, Non-Euclidean --- Hyperspace --- Relativity (Physics) --- Algebraic fields