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This book is a sequel to Lectures on Complex Analytic Varieties: The Local Paranwtrization Theorem (Mathematical Notes 10, 1970). Its unifying theme is the study of local properties of finite analytic mappings between complex analytic varieties; these mappings are those in several dimensions that most closely resemble general complex analytic mappings in one complex dimension. The purpose of this volume is rather to clarify some algebraic aspects of the local study of complex analytic varieties than merely to examine finite analytic mappings for their own sake.Originally published in 1970.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.

Complex analysis --- Analytic spaces --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Spaces, Analytic --- Analytic functions --- Functions of several complex variables --- Algebra homomorphism. --- Algebraic curve. --- Algebraic extension. --- Algebraic surface. --- Algebraic variety. --- Analytic continuation. --- Analytic function. --- Associated prime. --- Atlas (topology). --- Automorphism. --- Bernhard Riemann. --- Big O notation. --- Branch point. --- Change of variables. --- Characterization (mathematics). --- Codimension. --- Coefficient. --- Cohomology. --- Complete intersection. --- Complex analysis. --- Complex conjugate. --- Complex dimension. --- Complex number. --- Connected component (graph theory). --- Corollary. --- Critical point (mathematics). --- Diagram (category theory). --- Dimension (vector space). --- Dimension. --- Disjoint union. --- Divisor. --- Equation. --- Equivalence class. --- Exact sequence. --- Existential quantification. --- Finitely generated module. --- Geometry. --- Hamiltonian mechanics. --- Holomorphic function. --- Homeomorphism. --- Homological dimension. --- Homomorphism. --- Hypersurface. --- Ideal (ring theory). --- Identity element. --- Induced homomorphism. --- Inequality (mathematics). --- Injective function. --- Integral domain. --- Invertible matrix. --- Irreducible component. --- Isolated singularity. --- Isomorphism class. --- Jacobian matrix and determinant. --- Linear map. --- Linear subspace. --- Local ring. --- Mathematical induction. --- Mathematics. --- Maximal element. --- Maximal ideal. --- Meromorphic function. --- Modular arithmetic. --- Module (mathematics). --- Module homomorphism. --- Monic polynomial. --- Monomial. --- Neighbourhood (mathematics). --- Noetherian. --- Open set. --- Parametric equation. --- Parametrization. --- Permutation. --- Polynomial ring. --- Polynomial. --- Power series. --- Quadratic form. --- Quotient module. --- Regular local ring. --- Removable singularity. --- Ring (mathematics). --- Ring homomorphism. --- Row and column vectors. --- Scalar multiplication. --- Scientific notation. --- Several complex variables. --- Sheaf (mathematics). --- Special case. --- Subalgebra. --- Submanifold. --- Subset. --- Summation. --- Surjective function. --- Taylor series. --- Theorem. --- Three-dimensional space (mathematics). --- Topological space. --- Vector space. --- Weierstrass preparation theorem. --- Zero divisor. --- Fonctions de plusieurs variables complexes --- Variétés complexes

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Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.

Homotopie --- Homotopy theory --- Homotopy theory. --- Deformations, Continuous --- Topology --- Abelian category. --- Abelian group. --- Adams spectral sequence. --- Additive category. --- Affine space. --- Algebra homomorphism. --- Algebraic closure. --- Algebraic structure. --- Algebraic topology (object). --- Algebraic topology. --- Algebraic variety. --- Algebraically closed field. --- Atiyah–Hirzebruch spectral sequence. --- Automorphism. --- Boolean algebra (structure). --- CW complex. --- Canonical map. --- Cantor set. --- Category of topological spaces. --- Category theory. --- Classification theorem. --- Classifying space. --- Cohomology operation. --- Cohomology. --- Cokernel. --- Commutative algebra. --- Commutative ring. --- Complex projective space. --- Complex vector bundle. --- Computation. --- Conjecture. --- Conjugacy class. --- Continuous function. --- Contractible space. --- Coproduct. --- Differentiable manifold. --- Disjoint union. --- Division algebra. --- Equation. --- Explicit formulae (L-function). --- Functor. --- G-module. --- Groupoid. --- Homology (mathematics). --- Homomorphism. --- Homotopy category. --- Homotopy group. --- Homotopy. --- Hopf algebra. --- Hurewicz theorem. --- Inclusion map. --- Infinite product. --- Integer. --- Inverse limit. --- Irreducible representation. --- Isomorphism class. --- K-theory. --- Loop space. --- Mapping cone (homological algebra). --- Mathematical induction. --- Modular representation theory. --- Module (mathematics). --- Monomorphism. --- Moore space. --- Morava K-theory. --- Morphism. --- N-sphere. --- Noetherian ring. --- Noetherian. --- Noncommutative ring. --- Number theory. --- P-adic number. --- Piecewise linear manifold. --- Polynomial ring. --- Polynomial. --- Power series. --- Prime number. --- Principal ideal domain. --- Profinite group. --- Reduced homology. --- Ring (mathematics). --- Ring homomorphism. --- Ring spectrum. --- Simplicial complex. --- Simply connected space. --- Smash product. --- Special case. --- Spectral sequence. --- Steenrod algebra. --- Sub"ient. --- Subalgebra. --- Subcategory. --- Subring. --- Symmetric group. --- Tensor product. --- Theorem. --- Topological space. --- Topology. --- Vector bundle. --- Zariski topology.

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Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. The sixtieth birthday (on December 14, 1996) of C.T.C. Wall, a leading member of the subject's founding generation, led the editors of this volume to reflect on the extraordinary accomplishments of surgery theory as well as its current enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source surveying surgery theory and its applications. Because no one person could write such a survey, the editors asked a variety of experts to report on the areas of current interest. This is the second of two volumes resulting from that collective effort. It will be useful to topologists, to other interested researchers, and to advanced students. The topics covered include current applications of surgery, Wall's finiteness obstruction, algebraic surgery, automorphisms and embeddings of manifolds, surgery theoretic methods for the study of group actions and stratified spaces, metrics of positive scalar curvature, and surgery in dimension four. In addition to the editors, the contributors are S. Ferry, M. Weiss, B. Williams, T. Goodwillie, J. Klein, S. Weinberger, B. Hughes, S. Stolz, R. Kirby, L. Taylor, and F. Quinn.

Chirurgie (Topologie) --- Heelkunde (Topologie) --- Surgery (Topology) --- Differential topology --- Homotopy equivalences --- Manifolds (Mathematics) --- Topology --- Algebraic topology (object). --- Algebraic topology. --- Ambient isotopy. --- Assembly map. --- Atiyah–Hirzebruch spectral sequence. --- Atiyah–Singer index theorem. --- Automorphism. --- Banach algebra. --- Borsuk–Ulam theorem. --- C*-algebra. --- CW complex. --- Calculation. --- Category of manifolds. --- Characterization (mathematics). --- Chern class. --- Cobordism. --- Codimension. --- Cohomology. --- Compactification (mathematics). --- Conjecture. --- Contact geometry. --- Degeneracy (mathematics). --- Diagram (category theory). --- Diffeomorphism. --- Differentiable manifold. --- Differential geometry. --- Dirac operator. --- Disk (mathematics). --- Donaldson theory. --- Duality (mathematics). --- Embedding. --- Epimorphism. --- Excision theorem. --- Exponential map (Riemannian geometry). --- Fiber bundle. --- Fibration. --- Fundamental group. --- Group action. --- Group homomorphism. --- H-cobordism. --- Handle decomposition. --- Handlebody. --- Homeomorphism group. --- Homeomorphism. --- Homology (mathematics). --- Homomorphism. --- Homotopy extension property. --- Homotopy fiber. --- Homotopy group. --- Homotopy. --- Hypersurface. --- Intersection form (4-manifold). --- Intersection homology. --- Isomorphism class. --- K3 surface. --- L-theory. --- Limit (category theory). --- Manifold. --- Mapping cone (homological algebra). --- Mapping cylinder. --- Mostow rigidity theorem. --- Orthonormal basis. --- Parallelizable manifold. --- Poincaré conjecture. --- Product metric. --- Projection (linear algebra). --- Pushout (category theory). --- Quaternionic projective space. --- Quotient space (topology). --- Resolution of singularities. --- Ricci curvature. --- Riemann surface. --- Riemannian geometry. --- Riemannian manifold. --- Ring homomorphism. --- Scalar curvature. --- Semisimple algebra. --- Sheaf (mathematics). --- Sign (mathematics). --- Special case. --- Sub"ient. --- Subgroup. --- Submanifold. --- Support (mathematics). --- Surgery exact sequence. --- Surgery obstruction. --- Surgery theory. --- Symplectic geometry. --- Symplectic vector space. --- Theorem. --- Topological conjugacy. --- Topological manifold. --- Topology. --- Transversality (mathematics). --- Transversality theorem. --- Vector bundle. --- Waldhausen category. --- Whitehead torsion. --- Whitney embedding theorem. --- Yamabe invariant.

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This volume offers a systematic treatment of certain basic parts of algebraic geometry, presented from the analytic and algebraic points of view. The notes focus on comparison theorems between the algebraic, analytic, and continuous categories.Contents include: 1.1 sheaf theory, ringed spaces; 1.2 local structure of analytic and algebraic sets; 1.3 Pn 2.1 sheaves of modules; 2.2 vector bundles; 2.3 sheaf cohomology and computations on Pn; 3.1 maximum principle and Schwarz lemma on analytic spaces; 3.2 Siegel's theorem; 3.3 Chow's theorem; 4.1 GAGA; 5.1 line bundles, divisors, and maps to Pn; 5.2 Grassmanians and vector bundles; 5.3 Chern classes and curvature; 5.4 analytic cocycles; 6.1 K-theory and Bott periodicity; 6.2 K-theory as a generalized cohomology theory; 7.1 the Chern character and obstruction theory; 7.2 the Atiyah-Hirzebruch spectral sequence; 7.3 K-theory on algebraic varieties; 8.1 Stein manifold theory; 8.2 holomorphic vector bundles on polydisks; 9.1 concluding remarks; bibliography.Originally published in 1974.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.

Geometry, Algebraic --- Geometry, Analytic --- Additive map. --- Affine variety. --- Algebraic curve. --- Algebraic geometry. --- Algebraic operation. --- Algebraic surface. --- Algebraic variety. --- Analytic continuation. --- Analytic set. --- Analytic space. --- Atiyah–Hirzebruch spectral sequence. --- Automorphism. --- Bott periodicity theorem. --- Cauchy's integral formula. --- Chern class. --- Chow's theorem. --- Codimension. --- Coherence condition. --- Cohomology operation. --- Cohomology ring. --- Cohomology. --- Cokernel. --- Commutative diagram. --- Comparison theorem. --- Complex manifold. --- Complex vector bundle. --- De Rham cohomology. --- Diagram (category theory). --- Differentiable manifold. --- Differential form. --- Differential geometry. --- Differential topology. --- Dimension (vector space). --- Divisor (algebraic geometry). --- Divisor. --- Duality (mathematics). --- Epimorphism. --- Equation. --- Exact sequence. --- Fiber bundle. --- Fundamental class. --- General linear group. --- Grassmannian. --- Group homomorphism. --- Hilbert's syzygy theorem. --- Holomorphic function. --- Holomorphic sheaf. --- Holomorphic vector bundle. --- Homomorphism. --- Homotopy group. --- Homotopy. --- Irreducibility (mathematics). --- Isomorphism class. --- Jacobian matrix and determinant. --- K-theory. --- Laurent series. --- Lie derivative. --- Line bundle. --- Linear map. --- Manifold. --- Mathematical induction. --- Measure (mathematics). --- Meromorphic function. --- Module (mathematics). --- Morphism. --- Neighbourhood (mathematics). --- Obstruction theory. --- Polynomial. --- Power series. --- Presheaf (category theory). --- Principal bundle. --- Product topology. --- Projective space. --- Projective variety. --- Resolution of singularities. --- Riemann surface. --- Ring (mathematics). --- Ring homomorphism. --- Schwarz lemma. --- Sheaf (mathematics). --- Sheaf cohomology. --- Sheaf of modules. --- Simplicial complex. --- Special case. --- Spectral sequence. --- Stein manifold. --- Submanifold. --- Subset. --- Surjective function. --- Tangent bundle. --- Tangent space. --- Tensor algebra. --- Theorem. --- Topological space. --- Topology. --- Transcendence degree. --- Variable (mathematics). --- Vector bundle. --- Weierstrass preparation theorem. --- Zariski topology.

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Global analysis describes diverse yet interrelated research areas in analysis and algebraic geometry, particularly those in which Kunihiko Kodaira made his most outstanding contributions to mathematics. The eminent contributors to this volume, from Japan, the United States, and Europe, have prepared original research papers that illustrate the progress and direction of current research in complex variables and algebraic and differential geometry. The authors investigate, among other topics, complex manifolds, vector bundles, curved 4-dimensional space, and holomorphic mappings. Bibliographies facilitate further reading in the development of the various studies.Originally published in 1970.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.

Differential geometry. Global analysis --- Global analysis (Mathematics) --- Calculus of variations --- Differentiable manifolds --- 517.97 --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Calculus of variations. Mathematical theory of control --- Differentiable manifolds. --- Calculus of variations. --- Global analysis (Mathematics). --- 517.97 Calculus of variations. Mathematical theory of control --- Algebraic topology --- 514.7 --- -Calculus of variations --- #TCPW W3.0 --- #TCPW W3.2 --- #WWIS:MEET --- Differential manifolds --- Manifolds (Mathematics) --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Differential geometry. Algebraic and analytic methods in geometry --- 514.7 Differential geometry. Algebraic and analytic methods in geometry --- Addresses, essays, lectures --- Functional analysis --- Geometry --- Algebra homomorphism. --- Algebraic space. --- Associated graded ring. --- Automorphism. --- Betti number. --- Bilinear form. --- Canonical basis. --- Canonical bundle. --- Closed immersion. --- Codimension. --- Coefficient. --- Cohomology. --- Cokernel. --- Complete intersection. --- Complex manifold. --- Complex torus. --- Convex cone. --- Covering space. --- Dedekind domain. --- Deformation theory. --- Degenerate bilinear form. --- Diagram (category theory). --- Diffeomorphism. --- Differential form. --- Discrete group. --- Discrete valuation ring. --- Divisor. --- Elliptic operator. --- Elliptic surface. --- Endomorphism. --- Enriques surface. --- Epimorphism. --- Equation. --- Exact sequence. --- Existential quantification. --- Extremal length. --- Fiber bundle. --- Flat morphism. --- Frame bundle. --- Functor. --- Generic point. --- Grassmannian. --- Harmonic function. --- Heine–Borel theorem. --- Hensel's lemma. --- Holomorphic function. --- Homogeneous coordinates. --- Homomorphism. --- Hyperplane. --- Invertible sheaf. --- Kodaira embedding theorem. --- Kodaira vanishing theorem. --- Lie algebra. --- Line bundle. --- Linear independence. --- Linear map. --- Local ring. --- Mathematical induction. --- Meromorphic function. --- Metric space. --- Morphism. --- Natural number. --- Norm (mathematics). --- Normal extension. --- Normal subgroup. --- Open set. --- Orientability. --- Orthonormal basis. --- Partition of unity. --- Polynomial. --- Principal bundle. --- Principal homogeneous space. --- Projection (mathematics). --- Projective line. --- Quadric. --- Rational singularity. --- Residue field. --- Riemannian manifold. --- Ring homomorphism. --- Self-adjoint operator. --- Sheaf (mathematics). --- Sobolev space. --- Special case. --- Stokes' theorem. --- Subgroup. --- Submanifold. --- Subset. --- Subspace theorem. --- Summation. --- Surjective function. --- Symmetric tensor. --- Symplectic vector space. --- Tangent space. --- Theorem. --- Universal bundle. --- Upper and lower bounds. --- Vector bundle. --- Vector field. --- Wirtinger inequality (2-forms). --- Zariski topology. --- Analyse globale (mathématiques) --- Calcul des variations --- Analyse globale (mathématiques) --- Kodaira (kunihiko), mathematicien japonais, 1915 --- -Kodaira (kunihiko), mathematicien japonais, 1915 --- -517.97 --- -Analyse globale (mathématiques)