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In essence the proceedings of the 1967 meeting in Baton Rouge, the volume offers significant papers in the topology of infinite dimensional linear spaces, fixed point theory in infinite dimensional spaces, infinite dimensional differential topology, and infinite dimensional pointset topology. Later results of the contributors underscore the basic soundness of this selection, which includes survey and expository papers, as well as reports of continuing research.

Topology --- Differential geometry. Global analysis --- Differential topology --- Functional analysis --- Congresses --- Analyse fonctionnnelle --- Geometry, Differential --- Anderson's theorem. --- Annihilator (ring theory). --- Automorphism. --- Baire measure. --- Banach algebra. --- Banach manifold. --- Banach space. --- Bounded operator. --- Cartesian product. --- Characterization (mathematics). --- Cohomology. --- Compact space. --- Complement (set theory). --- Complete metric space. --- Connected space. --- Continuous function. --- Convex set. --- Coset. --- Critical point (mathematics). --- Diagram (category theory). --- Differentiable manifold. --- Differential topology. --- Dimension (vector space). --- Dimension. --- Dimensional analysis. --- Dual space. --- Duality (mathematics). --- Endomorphism. --- Equivalence class. --- Euclidean space. --- Existential quantification. --- Explicit formulae (L-function). --- Exponential map (Riemannian geometry). --- Fixed-point theorem. --- Fréchet derivative. --- Fréchet space. --- Fuchsian group. --- Function space. --- Fundamental class. --- Haar measure. --- Hessian matrix. --- Hilbert space. --- Homeomorphism. --- Homology (mathematics). --- Homotopy group. --- Homotopy. --- Inclusion map. --- Infimum and supremum. --- Lebesgue space. --- Lefschetz fixed-point theorem. --- Limit point. --- Linear space (geometry). --- Locally convex topological vector space. --- Loop space. --- Mathematical optimization. --- Measure (mathematics). --- Metric space. --- Module (mathematics). --- Natural topology. --- Neighbourhood (mathematics). --- Normal space. --- Normed vector space. --- Open set. --- Ordinal number. --- Paracompact space. --- Partition of unity. --- Path space. --- Product topology. --- Quantifier (logic). --- Quotient space (linear algebra). --- Quotient space (topology). --- Radon measure. --- Reflexive space. --- Representation theorem. --- Riemannian manifold. --- Schauder fixed point theorem. --- Sign (mathematics). --- Simply connected space. --- Space form. --- Special case. --- Stiefel manifold. --- Strong operator topology. --- Subcategory. --- Submanifold. --- Subset. --- Tangent space. --- Teichmüller space. --- Theorem. --- Topological space. --- Topological vector space. --- Topology. --- Transfinite induction. --- Transfinite. --- Transversal (geometry). --- Transversality theorem. --- Tychonoff cube. --- Union (set theory). --- Unit sphere. --- Weak topology. --- Weakly compact. --- Differential topology - Congresses --- Functional analysis - Congresses --- Topology - Congresses --- Analyse fonctionnelle.

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This work offers a contribution in the geometric form of the theory of several complex variables. Since complex Grassmann manifolds serve as classifying spaces of complex vector bundles, the cohomology structure of a complex Grassmann manifold is of importance for the construction of Chern classes of complex vector bundles. The cohomology ring of a Grassmannian is therefore of interest in topology, differential geometry, algebraic geometry, and complex analysis. Wilhelm Stoll treats certain aspects of the complex analysis point of view.This work originated with questions in value distribution theory. Here analytic sets and differential forms rather than the corresponding homology and cohomology classes are considered. On the Grassmann manifold, the cohomology ring is isomorphic to the ring of differential forms invariant under the unitary group, and each cohomology class is determined by a family of analytic sets.

Algebraic geometry --- Differential geometry. Global analysis --- Grassmann manifolds --- Differential forms. --- Grassmann manifolds. --- Invariants. --- Geometry, Differential. --- Géométrie différentielle. --- Differential invariants. --- Invariants différentiels. --- Forms, Differential --- Continuous groups --- Geometry, Differential --- Grassmannians --- Differential topology --- Manifolds (Mathematics) --- Calculation. --- Cohomology ring. --- Cohomology. --- Complex space. --- Cotangent bundle. --- Diagram (category theory). --- Exterior algebra. --- Grassmannian. --- Holomorphic vector bundle. --- Manifold. --- Regular map (graph theory). --- Remainder. --- Representation theorem. --- Schubert variety. --- Sesquilinear form. --- Theorem. --- Vector bundle. --- Vector space. --- Géométrie différentielle. --- Invariants différentiels.

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The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds.In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers.Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.

Algebraic topology --- Characteristic classes --- Classes caractéristiques --- 515.16 --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- Classes, Characteristic --- Differential topology --- Topology of manifolds --- Characteristic classes. --- 515.16 Topology of manifolds --- Classes caractéristiques --- Additive group. --- Axiom. --- Basis (linear algebra). --- Boundary (topology). --- Bundle map. --- CW complex. --- Canonical map. --- Cap product. --- Cartesian product. --- Characteristic class. --- Charles Ehresmann. --- Chern class. --- Classifying space. --- Coefficient. --- Cohomology ring. --- Cohomology. --- Compact space. --- Complex dimension. --- Complex manifold. --- Complex vector bundle. --- Complexification. --- Computation. --- Conformal geometry. --- Continuous function. --- Coordinate space. --- Cross product. --- De Rham cohomology. --- Diffeomorphism. --- Differentiable manifold. --- Differential form. --- Differential operator. --- Dimension (vector space). --- Dimension. --- Direct sum. --- Directional derivative. --- Eilenberg–Steenrod axioms. --- Embedding. --- Equivalence class. --- Euler class. --- Euler number. --- Existence theorem. --- Existential quantification. --- Exterior (topology). --- Fiber bundle. --- Fundamental class. --- Fundamental group. --- General linear group. --- Grassmannian. --- Gysin sequence. --- Hausdorff space. --- Homeomorphism. --- Homology (mathematics). --- Homotopy. --- Identity element. --- Integer. --- Interior (topology). --- Isomorphism class. --- J-homomorphism. --- K-theory. --- Leibniz integral rule. --- Levi-Civita connection. --- Limit of a sequence. --- Linear map. --- Metric space. --- Natural number. --- Natural topology. --- Neighbourhood (mathematics). --- Normal bundle. --- Open set. --- Orthogonal complement. --- Orthogonal group. --- Orthonormal basis. --- Partition of unity. --- Permutation. --- Polynomial. --- Power series. --- Principal ideal domain. --- Projection (mathematics). --- Representation ring. --- Riemannian manifold. --- Sequence. --- Singular homology. --- Smoothness. --- Special case. --- Steenrod algebra. --- Stiefel–Whitney class. --- Subgroup. --- Subset. --- Symmetric function. --- Tangent bundle. --- Tensor product. --- Theorem. --- Thom space. --- Topological space. --- Topology. --- Unit disk. --- Unit vector. --- Variable (mathematics). --- Vector bundle. --- Vector space. --- Topologie differentielle --- Classes caracteristiques --- Classes et nombres caracteristiques

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The classical uniformization theorem for Riemann surfaces and its recent extensions can be viewed as introducing special pseudogroup structures, affine or projective structures, on Riemann surfaces. In fact, the additional structures involved can be considered as local forms of the uniformizations of Riemann surfaces. In this study, Robert Gunning discusses the corresponding pseudogroup structures on higher-dimensional complex manifolds, modeled on the theory as developed for Riemann surfaces.Originally published in 1978.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.

Analytical spaces --- Differential geometry. Global analysis --- Complex manifolds --- Connections (Mathematics) --- Pseudogroups --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Global analysis (Mathematics) --- Lie groups --- Geometry, Differential --- Analytic spaces --- Manifolds (Mathematics) --- Adjunction formula. --- Affine connection. --- Affine transformation. --- Algebraic surface. --- Algebraic torus. --- Algebraic variety. --- Analytic continuation. --- Analytic function. --- Automorphic function. --- Automorphism. --- Bilinear form. --- Canonical bundle. --- Characterization (mathematics). --- Cohomology. --- Compact Riemann surface. --- Complex Lie group. --- Complex analysis. --- Complex dimension. --- Complex manifold. --- Complex multiplication. --- Complex number. --- Complex plane. --- Complex torus. --- Complex vector bundle. --- Contraction mapping. --- Covariant derivative. --- Differentiable function. --- Differentiable manifold. --- Differential equation. --- Differential form. --- Differential geometry. --- Differential operator. --- Dimension (vector space). --- Dimension. --- Elliptic operator. --- Elliptic surface. --- Enriques surface. --- Equation. --- Existential quantification. --- Explicit formula. --- Explicit formulae (L-function). --- Exterior derivative. --- Fiber bundle. --- General linear group. --- Geometric genus. --- Group homomorphism. --- Hausdorff space. --- Holomorphic function. --- Homomorphism. --- Identity matrix. --- Invariant subspace. --- Invertible matrix. --- Irreducible representation. --- Jacobian matrix and determinant. --- K3 surface. --- Kähler manifold. --- Lie algebra representation. --- Lie algebra. --- Line bundle. --- Linear equation. --- Linear map. --- Linear space (geometry). --- Linear subspace. --- Manifold. --- Mathematical analysis. --- Mathematical induction. --- Ordinary differential equation. --- Partial differential equation. --- Permutation. --- Polynomial. --- Principal bundle. --- Projection (linear algebra). --- Projective connection. --- Projective line. --- Pseudogroup. --- Quadratic transformation. --- Quotient space (topology). --- Representation theory. --- Riemann surface. --- Riemann–Roch theorem. --- Schwarzian derivative. --- Sheaf (mathematics). --- Special case. --- Subalgebra. --- Subgroup. --- Submanifold. --- Symmetric tensor. --- Symmetrization. --- Tangent bundle. --- Tangent space. --- Tensor field. --- Tensor product. --- Tensor. --- Theorem. --- Topological manifold. --- Uniformization theorem. --- Uniformization. --- Unit (ring theory). --- Vector bundle. --- Vector space. --- Fonctions de plusieurs variables complexes --- Variétés complexes

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The description for this book, Recent Developments in Several Complex Variables. (AM-100), Volume 100, will be forthcoming.

Complex analysis --- Functions of several complex variables. --- Complex variables --- Several complex variables, Functions of --- Functions of complex variables --- Analytic continuation. --- Analytic function. --- Analytic set. --- Analytic space. --- Asymptotic expansion. --- Automorphic function. --- Axiom. --- Base change. --- Bergman metric. --- Betti number. --- Big O notation. --- Bilinear form. --- Boundary value problem. --- CR manifold. --- Canonical bundle. --- Cauchy problem. --- Cauchy–Riemann equations. --- Characteristic variety. --- Codimension. --- Coefficient. --- Cohomology ring. --- Cohomology. --- Commutative property. --- Commutator. --- Compactification (mathematics). --- Complete intersection. --- Complete metric space. --- Complex dimension. --- Complex manifold. --- Complex number. --- Complex plane. --- Complex projective space. --- Complex space. --- Complex-analytic variety. --- Degeneracy (mathematics). --- Dense set. --- Determinant. --- Diffeomorphism. --- Differentiable function. --- Dimension (vector space). --- Dimension. --- Eigenvalues and eigenvectors. --- Embedding. --- Existential quantification. --- Explicit formulae (L-function). --- Fermat curve. --- Fiber bundle. --- Fundamental solution. --- Gorenstein ring. --- Hartogs' extension theorem. --- Hilbert space. --- Hilbert transform. --- Holomorphic function. --- Homotopy. --- Hyperfunction. --- Hypersurface. --- Hypoelliptic operator. --- Interpolation theorem. --- Irreducible component. --- Isometry. --- Linear map. --- Manifold. --- Maximal ideal. --- Monic polynomial. --- Monotonic function. --- Multiple integral. --- Nilpotent Lie algebra. --- Norm (mathematics). --- Open set. --- Orthogonal group. --- Parametrization. --- Permutation. --- Plurisubharmonic function. --- Polynomial. --- Principal bundle. --- Principal part. --- Principal value. --- Projection (linear algebra). --- Projective line. --- Proper map. --- Quadratic function. --- Real projective space. --- Resolution of singularities. --- Riemann surface. --- Riemannian manifold. --- Sectional curvature. --- Sheaf cohomology. --- Special case. --- Submanifold. --- Subset. --- Symplectic vector space. --- Tangent space. --- Theorem. --- Topology. --- Uniqueness theorem. --- Unit disk. --- Unit sphere. --- Variable (mathematics). --- Vector bundle. --- Vector field. --- Fonctions de variables complexes --- Colloque