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Book
Active galactic nuclei : from the central black hole to the galactic environment
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ISBN: 0691227470 Year: 1999 Publisher: Princeton, New Jersey : Princeton University Press,

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Abstract

This is the first comprehensive treatment of active galactic nuclei--the cosmic powerhouses at the core of many distant galaxies. The term active galactic nuclei refers to quasars, radio galaxies, Seyfert galaxies, blazars, and related objects, all of which are believed to share a similar central engine--a supermassive black hole many times the mass of the Sun. Astrophysicists have studied these phenomena for the past several decades and have begun to develop a consensus about many of their properties and internal mechanisms. Julian Krolik, one of the world's leading authorities on the subject, sums up leading ideas from across the entire range of research, making this book an invaluable resource for astronomers, physicists interested in applications of the theory of gravitation, and graduate students. Krolik begins by addressing basic questions about active galactic nuclei: What are they? How can they be found? How do they evolve? He assesses the evidence for massive black holes and considers how they generate power by accretion. He discusses X-ray and g-ray emission, radio emission and jets, emission and absorption lines, anisotropic appearance, and the relationship between an active nucleus and its host galaxy. He explores the mysteries of what ignites, fuels, and extinguishes active galactic nuclei, and concludes with a general review of where the field now stands. The book is unique in paying careful attention to relevant physics as well as astronomy, reflecting in part the importance of general relativity to understanding active galactic nuclei. Clear, authoritative, and detailed, this is crucial reading for anyone interested in one of the most dynamic areas of astrophysics today.


Book
Curvature and Betti Numbers. (AM-32), Volume 32
Authors: ---
ISBN: 1400882206 Year: 2016 Publisher: Princeton, NJ : Princeton University Press,

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The description for this book, Curvature and Betti Numbers. (AM-32), Volume 32, will be forthcoming.

Keywords

Curvature. --- Geometry, Differential. --- Abelian integral. --- Affine connection. --- Algebraic operation. --- Almost periodic function. --- Analytic function. --- Arc length. --- Betti number. --- Coefficient. --- Compact space. --- Complex analysis. --- Complex conjugate. --- Complex dimension. --- Complex manifold. --- Conservative vector field. --- Constant curvature. --- Constant function. --- Continuous function. --- Convex set. --- Coordinate system. --- Covariance and contravariance of vectors. --- Covariant derivative. --- Derivative. --- Differential form. --- Differential geometry. --- Dimension (vector space). --- Dimension. --- Einstein manifold. --- Equation. --- Euclidean domain. --- Euclidean geometry. --- Euclidean space. --- Existential quantification. --- Geometry. --- Hausdorff space. --- Hypersphere. --- Killing vector field. --- Kähler manifold. --- Lie group. --- Manifold. --- Metric tensor (general relativity). --- Metric tensor. --- Mixed tensor. --- One-parameter group. --- Orientability. --- Partial derivative. --- Periodic function. --- Permutation. --- Quantity. --- Ricci curvature. --- Riemannian manifold. --- Scalar (physics). --- Sectional curvature. --- Self-adjoint. --- Special case. --- Subset. --- Summation. --- Symmetric tensor. --- Symmetrization. --- Tensor algebra. --- Tensor calculus. --- Tensor field. --- Tensor. --- Theorem. --- Torsion tensor. --- Two-dimensional space. --- Uniform convergence. --- Uniform space. --- Unit circle. --- Unit sphere. --- Unit vector. --- Vector field.


Book
On Uniformization of Complex Manifolds : The Role of Connections (MN-22)
Author:
ISBN: 069108176X 1322884951 1400869307 0691636443 Year: 2015 Publisher: Princeton, NJ : Princeton University Press,

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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.

Keywords

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


Book
Morse Theory. (AM-51), Volume 51
Author:
ISBN: 1400881803 Year: 2016 Publisher: Princeton, NJ : Princeton University Press,

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One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his Topological Methods in the Theory of Functions of a Complex Variable in the Annals of Mathematics Studies series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory. Milnor was awarded the Fields Medal (the mathematical equivalent of a Nobel Prize) in 1962 for his work in differential topology. He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scienti.c disciplines. The citation reads, "The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor's writings. Reading his books, one is struck with the ease with which the subject is unfolding and it only becomes apparent after re.ection that this ease is the mark of a master.? Milnor has published five books with Princeton University Press.

Keywords

Homotopy theory. --- Geometry, Differential. --- Affine connection. --- Banach algebra. --- Betti number. --- Bott periodicity theorem. --- Bounded set. --- Calculus of variations. --- Cauchy sequence. --- Characteristic class. --- Clifford algebra. --- Compact space. --- Complex number. --- Conjugate points. --- Coordinate system. --- Corollary. --- Covariant derivative. --- Covering space. --- Critical point (mathematics). --- Curvature. --- Cyclic group. --- Derivative. --- Diagram (category theory). --- Diffeomorphism. --- Differentiable function. --- Differentiable manifold. --- Differential geometry. --- Differential structure. --- Differential topology. --- Dimension (vector space). --- Dirichlet problem. --- Elementary proof. --- Euclidean space. --- Euler characteristic. --- Exact sequence. --- Exponentiation. --- First variation. --- Function (mathematics). --- Fundamental lemma (Langlands program). --- Fundamental theorem. --- General position. --- Geometry. --- Great circle. --- Hessian matrix. --- Hilbert space. --- Homomorphism. --- Homotopy group. --- Homotopy. --- Implicit function theorem. --- Inclusion map. --- Infimum and supremum. --- Jacobi field. --- Lie algebra. --- Lie group. --- Line segment. --- Linear equation. --- Linear map. --- Loop space. --- Manifold. --- Mathematical induction. --- Metric connection. --- Metric space. --- Morse theory. --- N-sphere. --- Order of approximation. --- Orthogonal group. --- Orthogonal transformation. --- Paraboloid. --- Path space. --- Piecewise. --- Projective plane. --- Real number. --- Retract. --- Ricci curvature. --- Riemannian geometry. --- Riemannian manifold. --- Sard's theorem. --- Second fundamental form. --- Sectional curvature. --- Sequence. --- Simply connected space. --- Skew-Hermitian matrix. --- Smoothness. --- Special unitary group. --- Square-integrable function. --- Subgroup. --- Submanifold. --- Subset. --- Symmetric space. --- Tangent space. --- Tangent vector. --- Theorem. --- Topological group. --- Topological space. --- Topology. --- Torus. --- Unit sphere. --- Unit vector. --- Unitary group. --- Vector bundle. --- Vector field. --- Vector space.

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