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The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces.

Four-manifolds (Topology) --- Seiberg-Witten invariants. --- Mathematical physics. --- Physical mathematics --- Physics --- Invariants --- 4-dimensional manifolds (Topology) --- 4-manifolds (Topology) --- Four dimensional manifolds (Topology) --- Manifolds, Four dimensional --- Low-dimensional topology --- Topological manifolds --- Mathematics --- Affine space. --- Affine transformation. --- Algebra bundle. --- Algebraic surface. --- Almost complex manifold. --- Automorphism. --- Banach space. --- Clifford algebra. --- Cohomology. --- Cokernel. --- Complex dimension. --- Complex manifold. --- Complex plane. --- Complex projective space. --- Complex vector bundle. --- Complexification (Lie group). --- Computation. --- Configuration space. --- Conjugate transpose. --- Covariant derivative. --- Curvature form. --- Curvature. --- Differentiable manifold. --- Differential topology. --- Dimension (vector space). --- Dirac equation. --- Dirac operator. --- Division algebra. --- Donaldson theory. --- Duality (mathematics). --- Eigenvalues and eigenvectors. --- Elliptic operator. --- Elliptic surface. --- Equation. --- Fiber bundle. --- Frenet–Serret formulas. --- Gauge fixing. --- Gauge theory. --- Gaussian curvature. --- Geometry. --- Group homomorphism. --- Hilbert space. --- Hodge index theorem. --- Homology (mathematics). --- Homotopy. --- Identity (mathematics). --- Implicit function theorem. --- Intersection form (4-manifold). --- Inverse function theorem. --- Isomorphism class. --- K3 surface. --- Kähler manifold. --- Levi-Civita connection. --- Lie algebra. --- Line bundle. --- Linear map. --- Linear space (geometry). --- Linearization. --- Manifold. --- Mathematical induction. --- Moduli space. --- Multiplication theorem. --- Neighbourhood (mathematics). --- One-form. --- Open set. --- Orientability. --- Orthonormal basis. --- Parameter space. --- Parametric equation. --- Parity (mathematics). --- Partial derivative. --- Principal bundle. --- Projection (linear algebra). --- Pullback (category theory). --- Quadratic form. --- Quaternion algebra. --- Quotient space (topology). --- Riemann surface. --- Riemannian manifold. --- Sard's theorem. --- Sign (mathematics). --- Sobolev space. --- Spin group. --- Spin representation. --- Spin structure. --- Spinor field. --- Subgroup. --- Submanifold. --- Surjective function. --- Symplectic geometry. --- Symplectic manifold. --- Tangent bundle. --- Tangent space. --- Tensor product. --- Theorem. --- Three-dimensional space (mathematics). --- Trace (linear algebra). --- Transversality (mathematics). --- Two-form. --- Zariski tangent space.

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The utility idea has had a long history in economics, especially in the explanation of demand and in welfare economics. In a comprehensive survey and critique of the Slutsky theory and the pattern to which it belongs in the economic context, S. N. Afriat offers a resolution of questions central to its main idea, including sufficient conditions as well.Originally published in 1980.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Demand functions (Economic theory) --- Utility theory --- 330.105 --- 338.5 --- Demand (Economic theory) --- Value --- Revealed preference theory --- Demand curves (Economic theory) --- Functions, Demand (Economic theory) --- Economics --- 330.105 Wiskundige economie. Wiskundige methoden in de economie --- Wiskundige economie. Wiskundige methoden in de economie --- 338.5 Prijsvorming. Prijskostenverhouding. Prijsbeweging. Prijsfluctuatie--macroeconomisch; prijsindex zie {336.748.12} --- Prijsvorming. Prijskostenverhouding. Prijsbeweging. Prijsfluctuatie--macroeconomisch; prijsindex zie {336.748.12} --- Mathematical models --- Quantitative methods (economics) --- E-books --- Utility theory. --- DEMAND FUNCTIONS (Economic theory) --- Adjoint. --- Aggregate supply. --- Arrow's impossibility theorem. --- Axiom. --- Big O notation. --- Bruno de Finetti. --- Chain rule. --- Coefficient. --- Commodity. --- Concave function. --- Continuous function. --- Convex cone. --- Convex function. --- Convex set. --- Corollary. --- Cost curve. --- Cost-effectiveness analysis. --- Cost–benefit analysis. --- Counterexample. --- Demand curve. --- Derivative. --- Determinant. --- Differentiable function. --- Differential calculus. --- Differential equation. --- Differential form. --- Divisia index. --- Economic equilibrium. --- Economics. --- Einstein notation. --- Equivalence relation. --- Explicit formulae (L-function). --- Factorization. --- Frobenius theorem (differential topology). --- Function (mathematics). --- Functional equation. --- General equilibrium theory. --- Heine–Borel theorem. --- Hessian matrix. --- Homogeneous function. --- Idempotence. --- Identity (mathematics). --- Identity matrix. --- Inequality (mathematics). --- Inference. --- Infimum and supremum. --- Integrating factor. --- Interdependence. --- Interval (mathematics). --- Inverse demand function. --- Inverse function theorem. --- Inverse function. --- Invertible matrix. --- Lagrange multiplier. --- Lagrangian (field theory). --- Lagrangian. --- Law of demand. --- Limit point. --- Line segment. --- Linear function. --- Linear inequality. --- Linear map. --- Linearity. --- Logical disjunction. --- Marginal cost. --- Mathematical induction. --- Mathematical optimization. --- Maxima and minima. --- Monotonic function. --- Ordinary differential equation. --- Orthogonal complement. --- Oskar Morgenstern. --- Pareto efficiency. --- Partial derivative. --- Permutation. --- Preference (economics). --- Price index. --- Principal part. --- Production function. --- Production theory. --- Quasiconvex function. --- Recursive definition. --- Reductio ad absurdum. --- Regular matrix. --- Requirement. --- Row and column vectors. --- Samuelson condition. --- Second derivative. --- Sign (mathematics). --- Special case. --- Statistic. --- Support function. --- Symmetric relation. --- Theorem. --- Theory. --- Transpose. --- Upper and lower bounds. --- Utility. --- Variable (mathematics). --- Welfare economics.