Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

So-called classical logic--the logic developed in the early twentieth century by Gottlob Frege, Bertrand Russell, and others--is computationally the simplest of the major logics, and it is adequate for the needs of most mathematicians. But it is just one of the many kinds of reasoning in everyday thought. Consequently, when presented by itself--as in most introductory texts on logic--it seems arbitrary and unnatural to students new to the subject. In Classical and Nonclassical Logics, Eric Schechter introduces classical logic alongside constructive, relevant, comparative, and other nonclassical logics. Such logics have been investigated for decades in research journals and advanced books, but this is the first textbook to make this subject accessible to beginners. While presenting an assortment of logics separately, it also conveys the deeper ideas (such as derivations and soundness) that apply to all logics. The book leads up to proofs of the Disjunction Property of constructive logic and completeness for several logics. The book begins with brief introductions to informal set theory and general topology, and avoids advanced algebra; thus it is self-contained and suitable for readers with little background in mathematics. It is intended primarily for undergraduate students with no previous experience of formal logic, but advanced students as well as researchers will also profit from this book.

Mathematics --- Proposition (Logic) --- Philosophy. --- Ackermann constants. --- Banach-Tarski paradox. --- Brouwer. --- Eubulides paradox. --- Herbrand Principle. --- Heyting algebras. --- Jarden's Proof. --- adequacy. --- algorithm. --- ambiguity. --- binary operator. --- certification. --- chain order. --- comparative logic. --- consequence. --- derivation. --- detachment. --- discrete topology. --- equivalence class. --- excluded middle. --- extremes. --- functional interpretation. --- fuzzy logics. --- generated topology. --- homomorphism. --- idempotency. --- implication. --- informal set theory. --- lower set topology. --- monotone. --- natural numbers. --- parentheses. --- quantifier. --- semantic. --- symbol sharing. --- tautology.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

One of the great achievements of contemporary mathematics is the new understanding of four dimensions. Michael Freedman and Frank Quinn have been the principals in the geometric and topological development of this subject, proving the Poincar and Annulus conjectures respectively. Recognition for this work includes the award of the Fields Medal of the International Congress of Mathematicians to Freedman in 1986. In Topology of 4-Manifolds these authors have collaborated to give a complete and accessible account of the current state of knowledge in this field. The basic material has been considerably simplified from the original publications, and should be accessible to most graduate students. The advanced material goes well beyond the literature; nearly one-third of the book is new. This work is indispensable for any topologist whose work includes four dimensions. It is a valuable reference for geometers and physicists who need an awareness of the topological side of the field.Originally published in 1990.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 topology --- Four-manifolds (Topology) --- Trois-variétés (Topologie) --- Vier-menigvuldigheden (Topologie) --- 4-dimensional manifolds (Topology) --- 4-manifolds (Topology) --- Four dimensional manifolds (Topology) --- Manifolds, Four dimensional --- Low-dimensional topology --- Topological manifolds --- 4-manifold. --- Ambient isotopy. --- Annulus theorem. --- Automorphism. --- Baire category theorem. --- Bilinear form. --- Boundary (topology). --- CW complex. --- Category of manifolds. --- Central series. --- Characterization (mathematics). --- Cohomology. --- Commutative diagram. --- Commutative property. --- Commutator subgroup. --- Compactification (mathematics). --- Conformal geometry. --- Connected sum. --- Connectivity (graph theory). --- Cyclic group. --- Diagram (category theory). --- Diameter. --- Diffeomorphism. --- Differentiable manifold. --- Differential geometry. --- Dimension. --- Disk (mathematics). --- Duality (mathematics). --- Eigenvalues and eigenvectors. --- Embedding problem. --- Embedding. --- Equivariant map. --- Fiber bundle. --- Four-dimensional space. --- Fundamental group. --- General position. --- Geometry. --- H-cobordism. --- Handlebody. --- Hauptvermutung. --- Homeomorphism. --- Homology (mathematics). --- Homology sphere. --- Homomorphism. --- Homotopy group. --- Homotopy sphere. --- Homotopy. --- Hurewicz theorem. --- Hyperbolic geometry. --- Hyperbolic group. --- Hyperbolic manifold. --- Identity matrix. --- Intermediate value theorem. --- Intersection (set theory). --- Intersection curve. --- Intersection form (4-manifold). --- Intersection number (graph theory). --- Intersection number. --- J-homomorphism. --- Knot theory. --- Lefschetz duality. --- Line–line intersection. --- Manifold. --- Mapping cylinder. --- Mathematical induction. --- Metric space. --- Metrization theorem. --- Module (mathematics). --- Normal bundle. --- Parametrization. --- Parity (mathematics). --- Product topology. --- Pullback (differential geometry). --- Regular homotopy. --- Ring homomorphism. --- Rotation number. --- Seifert–van Kampen theorem. --- Sesquilinear form. --- Set (mathematics). --- Simply connected space. --- Smooth structure. --- Special case. --- Spin structure. --- Submanifold. --- Subset. --- Support (mathematics). --- Tangent bundle. --- Tangent space. --- Tensor product. --- Theorem. --- Topological category. --- Topological manifold. --- Transversal (geometry). --- Transversality (mathematics). --- Transversality theorem. --- Uniqueness theorem. --- Unit disk. --- Vector bundle. --- Whitehead torsion. --- Whitney disk.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.