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Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area.The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.

Differential geometry. Global analysis --- Manifolds (Mathematics) --- Piecewise linear topology --- Triangulating manifolds --- Variétés (Mathématiques) --- Topologie linéaire par morceaux --- 515.16 --- Manifolds, Triangulating --- PL topology --- Topology --- Geometry, Differential --- Topology of manifolds --- Piecewise linear topology. --- Triangulating manifolds. --- Manifolds (Mathematics). --- 515.16 Topology of manifolds --- Variétés (Mathématiques) --- Topologie linéaire par morceaux --- Triangulation. --- Triangulation --- Affine space. --- Algebraic topology (object). --- Approximation. --- Associative property. --- Automorphism. --- Big O notation. --- CW complex. --- Calculation. --- Cap product. --- Cartesian product. --- Category of sets. --- Chain complex. --- Classification theorem. --- Classifying space. --- Cobordism. --- Codimension. --- Cofibration. --- Cohomology. --- Connected space. --- Continuous function (set theory). --- Continuous function. --- Counterexample. --- Diffeomorphism. --- Differentiable manifold. --- Differential structure. --- Differential topology. --- Dimension (vector space). --- Direct proof. --- Disjoint union. --- Elementary proof. --- Embedding. --- Euclidean space. --- Existence theorem. --- Existential quantification. --- Fiber bundle. --- Fibration. --- General position. --- Geometry. --- Group homomorphism. --- H-cobordism. --- H-space. --- Handle decomposition. --- Handlebody. --- Hauptvermutung. --- Hausdorff space. --- Hilbert cube. --- Homeomorphism group. --- Homeomorphism. --- Homomorphism. --- Homotopy group. --- Homotopy. --- Inclusion map. --- Injective function. --- Invertible matrix. --- K-cell (mathematics). --- Kan extension. --- Linear subspace. --- Linear topology. --- Manifold. --- Mapping cylinder. --- Mathematical induction. --- Mathematician. --- Metric space. --- Morse theory. --- Neighbourhood (mathematics). --- Open set. --- Partition of unity. --- Piecewise linear manifold. --- Piecewise linear. --- Poincaré conjecture. --- Polyhedron. --- Principal bundle. --- Product metric. --- Pushout (category theory). --- Regular homotopy. --- Retract. --- Sheaf (mathematics). --- Simplicial complex. --- Smoothing. --- Spin structure. --- Stability theory. --- Stable manifold. --- Standard map. --- Submanifold. --- Submersion (mathematics). --- Subset. --- Surgery exact sequence. --- Surjective function. --- Theorem. --- Topological group. --- Topological manifold. --- Topological space. --- Topology. --- Transversal (geometry). --- Transversality (mathematics). --- Transversality theorem. --- Union (set theory). --- Uniqueness theorem. --- Vector bundle. --- Zorn's lemma. --- Variétés topologiques

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Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically. It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.

#WWIS:d.d. Prof. L. Bouckaert/ALTO --- 515.1 --- 515.1 Topology --- Topology --- Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Algebraic topology. --- Associated bundle. --- Associative algebra. --- Associative property. --- Atlas (topology). --- Automorphism. --- Axiomatic system. --- Barycentric subdivision. --- Bilinear map. --- Bundle map. --- Classification theorem. --- Coefficient. --- Cohomology ring. --- Cohomology. --- Conjugacy class. --- Connected component (graph theory). --- Connected space. --- Coordinate system. --- Coset. --- Cup product. --- Cyclic group. --- Determinant. --- Differentiable manifold. --- Differential structure. --- Dimension (vector space). --- Direct product. --- Division algebra. --- Equivalence class. --- Equivalence relation. --- Euler number. --- Existence theorem. --- Existential quantification. --- Factorization. --- Fiber bundle. --- Frenet–Serret formulas. --- Gram–Schmidt process. --- Group theory. --- Homeomorphism. --- Homology (mathematics). --- Homomorphism. --- Homotopy group. --- Homotopy. --- Hopf theorem. --- Hurewicz theorem. --- Identity element. --- Inclusion map. --- Inner automorphism. --- Invariant subspace. --- Invertible matrix. --- Jacobian matrix and determinant. --- Klein bottle. --- Lattice of subgroups. --- Lie group. --- Line element. --- Line segment. --- Linear map. --- Linear space (geometry). --- Linear subspace. --- Manifold. --- Mapping cylinder. --- Metric tensor. --- N-sphere. --- Natural topology. --- Octonion. --- Open set. --- Orientability. --- Orthogonal group. --- Orthogonalization. --- Permutation. --- Principal bundle. --- Product topology. --- Quadratic form. --- Quaternion. --- Retract. --- Separable space. --- Set theory. --- Simplicial complex. --- Special case. --- Stiefel manifold. --- Subalgebra. --- Subbase. --- Subgroup. --- Subset. --- Symmetric tensor. --- Tangent bundle. --- Tangent space. --- Tangent vector. --- Tensor field. --- Tensor. --- Theorem. --- Tietze extension theorem. --- Topological group. --- Topological space. --- Transitive relation. --- Transpose. --- Union (set theory). --- Unit sphere. --- Universal bundle. --- Vector field.

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Rabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter-dependent families of nonlinear equations, uses topological methods that address the problem of continuous parameter dependence of solutions by showing that there are connected sets of solutions of global extent. Even when the operators are infinitely differentiable in all the variables and parameters, connectedness here cannot in general be replaced by path-connectedness. However, in the context of real-analyticity there is an alternative theory of global bifurcation due to Dancer, which offers a much stronger notion of parameter dependence. This book aims to develop from first principles Dancer's global bifurcation theory for one-parameter families of real-analytic operators in Banach spaces. It shows that there are globally defined continuous and locally real-analytic curves of solutions. In particular, in the real-analytic setting, local analysis can lead to global consequences--for example, as explained in detail here, those resulting from bifurcation from a simple eigenvalue. Included are accounts of analyticity and implicit function theorems in Banach spaces, classical results from the theory of finite-dimensional analytic varieties, and the links between these two and global existence theory. Laying the foundations for more extensive studies of real-analyticity in infinite-dimensional problems and illustrating the theory with examples, Analytic Theory of Global Bifurcation is intended for graduate students and researchers in pure and applied analysis.

Differential geometry. Global analysis --- Bifurcation theory. --- Differential equations, Nonlinear --- Stability --- Numerical solutions --- Addition. --- Algebraic equation. --- Analytic function. --- Analytic manifold. --- Atmospheric pressure. --- Banach space. --- Bernhard Riemann. --- Bifurcation diagram. --- Boundary value problem. --- Bounded operator. --- Bounded set (topological vector space). --- Boundedness. --- Canonical form. --- Cartesian coordinate system. --- Codimension. --- Compact operator. --- Complex analysis. --- Complex conjugate. --- Complex number. --- Connected space. --- Coordinate system. --- Corollary. --- Curvature. --- Derivative. --- Diagram (category theory). --- Differentiable function. --- Differentiable manifold. --- Dimension (vector space). --- Dimension. --- Direct sum. --- Eigenvalues and eigenvectors. --- Elliptic integral. --- Embedding. --- Equation. --- Euclidean division. --- Euler equations (fluid dynamics). --- Existential quantification. --- First principle. --- Fredholm operator. --- Froude number. --- Functional analysis. --- Hilbert space. --- Homeomorphism. --- Implicit function theorem. --- Integer. --- Linear algebra. --- Linear function. --- Linear independence. --- Linear map. --- Linear programming. --- Linear space (geometry). --- Linear subspace. --- Linearity. --- Linearization. --- Metric space. --- Morse theory. --- Multilinear form. --- N0. --- Natural number. --- Neumann series. --- Nonlinear functional analysis. --- Nonlinear system. --- Numerical analysis. --- Open mapping theorem (complex analysis). --- Operator (physics). --- Ordinary differential equation. --- Parameter. --- Parametrization. --- Partial differential equation. --- Permutation group. --- Permutation. --- Polynomial. --- Power series. --- Prime number. --- Proportionality (mathematics). --- Pseudo-differential operator. --- Puiseux series. --- Quantity. --- Real number. --- Resultant. --- Singularity theory. --- Skew-symmetric matrix. --- Smoothness. --- Solution set. --- Special case. --- Standard basis. --- Sturm–Liouville theory. --- Subset. --- Symmetric bilinear form. --- Symmetric group. --- Taylor series. --- Taylor's theorem. --- Theorem. --- Total derivative. --- Two-dimensional space. --- Union (set theory). --- Variable (mathematics). --- Vector space. --- Zero of a function.

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This book contains the lectures presented at a conference held at Princeton University in May 1991 in honor of Elias M. Stein's sixtieth birthday. The lectures deal with Fourier analysis and its applications. The contributors to the volume are W. Beckner, A. Boggess, J. Bourgain, A. Carbery, M. Christ, R. R. Coifman, S. Dobyinsky, C. Fefferman, R. Fefferman, Y. Han, D. Jerison, P. W. Jones, C. Kenig, Y. Meyer, A. Nagel, D. H. Phong, J. Vance, S. Wainger, D. Watson, G. Weiss, V. Wickerhauser, and T. H. Wolff.The topics of the lectures are: conformally invariant inequalities, oscillatory integrals, analytic hypoellipticity, wavelets, the work of E. M. Stein, elliptic non-smooth PDE, nodal sets of eigenfunctions, removable sets for Sobolev spaces in the plane, nonlinear dispersive equations, bilinear operators and renormalization, holomorphic functions on wedges, singular Radon and related transforms, Hilbert transforms and maximal functions on curves, Besov and related function spaces on spaces of homogeneous type, and counterexamples with harmonic gradients in Euclidean space.Originally published in 1995.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.

Fourier analysis --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Congresses --- Analysis, Fourier --- -Analysis, Fourier --- -Theory of the Fourier integral --- -517.518.5 Theory of the Fourier integral --- 517.518.5 --- 517.518.5 Theory of the Fourier integral --- Theory of the Fourier integral --- Mathematical analysis --- Analytic function. --- Banach fixed-point theorem. --- Bessel function. --- Blaschke product. --- Boundary value problem. --- Bounded operator. --- Cauchy–Riemann equations. --- Coefficient. --- Commutative property. --- Convolution. --- Degeneracy (mathematics). --- Differential equation. --- Differential geometry. --- Differential operator. --- Dirichlet problem. --- Distribution (mathematics). --- Eigenvalues and eigenvectors. --- Elias M. Stein. --- Elliptic integral. --- Elliptic operator. --- Equation. --- Ergodic theory. --- Error analysis (mathematics). --- Estimation. --- Existential quantification. --- Fourier analysis. --- Fourier integral operator. --- Fourier series. --- Fourier transform. --- Fundamental matrix (linear differential equation). --- Fundamental solution. --- Geometry. --- Green's function. --- Haar measure. --- Hardy space. --- Hardy–Littlewood maximal function. --- Harmonic analysis. --- Harmonic function. --- Harmonic measure. --- Hausdorff dimension. --- Heisenberg group. --- Hermitian matrix. --- Hilbert space. --- Hilbert transform. --- Holomorphic function. --- Hopf lemma. --- Hyperbolic partial differential equation. --- Integral geometry. --- Integral transform. --- Julia set. --- Korteweg–de Vries equation. --- Lagrangian (field theory). --- Lebesgue differentiation theorem. --- Lebesgue measure. --- Lie algebra. --- Linear map. --- Lipschitz continuity. --- Lipschitz domain. --- Mandelbrot set. --- Martingale (probability theory). --- Mathematical analysis. --- Maximal function. --- Measurable Riemann mapping theorem. --- Minkowski space. --- Misiurewicz point. --- Morera's theorem. --- Möbius transformation. --- Nilpotent group. --- Non-Euclidean geometry. --- Numerical analysis. --- Nyquist–Shannon sampling theorem. --- Ordinary differential equation. --- Orthonormal basis. --- Orthonormal frame. --- Oscillatory integral. --- Partial differential equation. --- Plurisubharmonic function. --- Pseudo-Riemannian manifold. --- Pseudo-differential operator. --- Pythagorean theorem. --- Radon transform. --- Regularity theorem. --- Representation theory. --- Riemannian manifold. --- Riesz representation theorem. --- Riesz transform. --- Schrödinger equation. --- Schwartz kernel theorem. --- Sign (mathematics). --- Simultaneous equations. --- Singular integral. --- Sobolev inequality. --- Sobolev space. --- Special case. --- Symmetrization. --- Theorem. --- Trigonometric series. --- Uniqueness theorem. --- Variable (mathematics). --- Variational inequality. --- Analyse harmonique