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This book is unique compared to the existing literature. It is very didactical and accessible to both students and researchers, without neglecting the formal character and the deep algebraic completeness of the topic along with its physical applications.
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Voyages and travels. --- Navigation. --- Voyages and travels --- Early maps. --- Cavendish, Thomas, --- Cumberland, George Clifford, --- Davis, John,
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This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration. A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds.
Algebres de Clifford --- Clifford [Algebra's van ] --- Clifford algebras --- Fysica [Mathematische ] --- Fysica [Wiskundige ] --- Mathematische fysica --- Physics -- Mathematics --- Physics [Mathematical ] --- Physique -- Mathématiques --- Physique -- Méthodes mathématiques --- Wiskundige fysica --- Clifford, Algèbres de --- Spin, Nuclear --- Geometric algebras --- Clifford algebras. --- Spin geometry. --- Clifford, Algèbres de --- Spin geometry --- 514.76 --- Algebras, Linear --- 514.76 Geometry of differentiable manifolds and of their submanifolds --- Geometry of differentiable manifolds and of their submanifolds --- Global differential geometry --- Geometry --- Mathematical physics --- Topology --- Nuclear spin --- -Mathematics --- Géométrie --- Physique mathématique --- Spin nucléaire --- Topologie --- Mathematics --- Mathématiques --- Algebraic theory. --- Atiyah–Singer index theorem. --- Automorphism. --- Betti number. --- Binary icosahedral group. --- Binary octahedral group. --- Bundle metric. --- C*-algebra. --- Calabi conjecture. --- Calabi–Yau manifold. --- Cartesian product. --- Classification theorem. --- Clifford algebra. --- Cobordism. --- Cohomology ring. --- Cohomology. --- Cokernel. --- Complete metric space. --- Complex manifold. --- Complex vector bundle. --- Complexification (Lie group). --- Covering space. --- Diffeomorphism. --- Differential topology. --- Dimension (vector space). --- Dimension. --- Dirac operator. --- Disk (mathematics). --- Dolbeault cohomology. --- Einstein field equations. --- Elliptic operator. --- Equivariant K-theory. --- Exterior algebra. --- Fiber bundle. --- Fixed-point theorem. --- Fourier inversion theorem. --- Fundamental group. --- Gauge theory. --- Geometry. --- Hilbert scheme. --- Holonomy. --- Homotopy sphere. --- Homotopy. --- Hyperbolic manifold. --- Induced homomorphism. --- Intersection form (4-manifold). --- Isomorphism class. --- J-invariant. --- K-theory. --- Kähler manifold. --- Laplace operator. --- Lie algebra. --- Lorentz covariance. --- Lorentz group. --- Manifold. --- Mathematical induction. --- Metric connection. --- Minkowski space. --- Module (mathematics). --- N-sphere. --- Operator (physics). --- Orthonormal basis. --- Principal bundle. --- Projective space. --- Pseudo-Riemannian manifold. --- Pseudo-differential operator. --- Quadratic form. --- Quaternion. --- Quaternionic projective space. --- Ricci curvature. --- Riemann curvature tensor. --- Riemannian geometry. --- Riemannian manifold. --- Ring homomorphism. --- Scalar curvature. --- Scalar multiplication. --- Sign (mathematics). --- Space form. --- Sphere theorem. --- Spin representation. --- Spin structure. --- Spinor bundle. --- Spinor field. --- Spinor. --- Subgroup. --- Support (mathematics). --- Symplectic geometry. --- Tangent bundle. --- Tangent space. --- Tensor calculus. --- Tensor product. --- Theorem. --- Topology. --- Unit disk. --- Unit sphere. --- Variable (mathematics). --- Vector bundle. --- Vector field. --- Vector space. --- Volume form. --- Nuclear spin - - Mathematics --- -Clifford algebras.
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The last major collective Abstract Expressionism exhibition in the UK took place in 1959. This publication, and the exhibition it accompanies, examines the origins of the movement and seeks to re-evaluate it, recognising its complex and fluid reality, and encompassing sculptors as well as some of the most famous painters of the twentieth century.
kunst --- Pollock Jackson --- de Kooning Willem --- Rothko Mark --- Still Clifford --- Mitchell joan --- Kline Franz --- Nevelson Louise --- Smith David --- beeldhouwkunst --- Siskind Aaron --- Morgan Barbara --- White Minor --- fotografie --- 75.036 --- action painting --- abstract expressionisme --- abstracte schilderkunst --- Verenigde Staten --- Parsons Betty --- Guggenheim Peggy --- abstractie --- twintigste eeuw --- schilderkunst --- Exhibitions --- Art, Abstract --- Abstract expressionism --- Art, Modern --- Abstrakter Expressionismus --- Abstract expressionism. --- Art abstrait --- Expressionnisme abstrait --- Art --- Exhibitions. --- Expositions --- feminisme --- kunsthandel --- vrouwen --- Guggenheim, Peggy --- Parsons, Betty --- Abstract Expressionist --- Art styles --- anno 1940-1949 --- anno 1950-1959 --- vrouw --- abstract expressionisme. --- feminisme. --- kunsthandel. --- vrouw. --- Guggenheim, Peggy. --- Parsons, Betty.
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The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.
Cartes harmoniques --- Harmonic maps --- Harmonische kaarten --- Immersies (Wiskunde) --- Immersions (Mathematics) --- Immersions (Mathématiques) --- Harmonic maps. --- Differential equations, Elliptic --- Applications harmoniques --- Immersions (Mathematiques) --- Équations différentielles elliptiques --- Numerical solutions. --- Solutions numériques --- Équations différentielles elliptiques --- Solutions numériques --- Differential equations [Elliptic] --- Numerical solutions --- Embeddings (Mathematics) --- Manifolds (Mathematics) --- Mappings (Mathematics) --- Maps, Harmonic --- Arc length. --- Catenary. --- Clifford algebra. --- Codimension. --- Coefficient. --- Compact space. --- Complex projective space. --- Connected sum. --- Constant curvature. --- Corollary. --- Covariant derivative. --- Curvature. --- Cylinder (geometry). --- Degeneracy (mathematics). --- Diagram (category theory). --- Differential equation. --- Differential geometry. --- Elliptic partial differential equation. --- Embedding. --- Energy functional. --- Equation. --- Existence theorem. --- Existential quantification. --- Fiber bundle. --- Gauss map. --- Geometry and topology. --- Geometry. --- Gravitational field. --- Harmonic map. --- Hyperbola. --- Hyperplane. --- Hypersphere. --- Hypersurface. --- Integer. --- Iterative method. --- Levi-Civita connection. --- Lie group. --- Mathematics. --- Maximum principle. --- Mean curvature. --- Normal (geometry). --- Numerical analysis. --- Open set. --- Ordinary differential equation. --- Parabola. --- Quadratic form. --- Sign (mathematics). --- Special case. --- Stiefel manifold. --- Submanifold. --- Suggestion. --- Surface of revolution. --- Symmetry. --- Tangent bundle. --- Theorem. --- Vector bundle. --- Vector space. --- Vertical tangent. --- Winding number. --- Differential equations, Elliptic - Numerical solutions
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What do we mean when we say that a novel's conclusion "feels right"? How did feeling, form, and the sense of right and wrong get mixed up, during the nineteenth century, in the experience of reading a novel? Good Form argues that Victorian readers associated the feeling of narrative form-of being pulled forward to a satisfying conclusion-with inner moral experience. Reclaiming the work of a generation of Victorian "intuitionist" philosophers who insisted that true morality consisted in being able to feel or intuit the morally good, Jesse Rosenthal shows that when Victorians discussed the moral dimensions of reading novels, they were also subtly discussing the genre's formal properties.For most, Victorian moralizing is one of the period's least attractive and interesting qualities. But Good Form argues that the moral interpretation of novel experience was essential in the development of the novel form-and that this moral approach is still a fundamental, if unrecognized, part of how we understand novels. Bringing together ideas from philosophy, literary history, and narrative theory, Rosenthal shows that we cannot understand the formal principles of the novel that we have inherited from the nineteenth century without also understanding the moral principles that have come with them. Good Form helps us to understand the way Victorians read, but it also helps us to understand the way we read now.
Ethics in literature. --- English fiction --- History and criticism. --- 1800-1899 --- Analogy. --- Anecdote. --- Autobiography. --- Backstory. --- Bildungsroman. --- Cambridge University Press. --- Character (arts). --- Charles Dickens. --- Conscience. --- Consciousness. --- Crime fiction. --- Criticism. --- Critique of Pure Reason. --- D. A. Miller. --- Daniel Deronda. --- Deus ex machina. --- E. M. Forster. --- Edward Bulwer-Lytton. --- Elizabeth Gaskell. --- Epic poetry. --- Ethics. --- Eugene Aram. --- Explanation. --- Fiction. --- Franco Moretti. --- Fredric Jameson. --- Genre fiction. --- Genre. --- George Eliot. --- George Meredith. --- Good and evil. --- Groundwork of the Metaphysic of Morals. --- Gwendolen Harleth. --- Gwendolen. --- Halpern. --- Historical fiction. --- Humour. --- I Wish (manhwa). --- Ian Watt. --- Illustration. --- Intuitionism. --- Jack Sheppard. --- James Clerk Maxwell. --- John Stuart Mill. --- Johns Hopkins. --- Jonathan Wild. --- Laughter. --- Lecture. --- Leopold Zunz. --- Literary criticism. --- Literary realism. --- Literature. --- Mary Barton. --- Meditations. --- Middlemarch. --- Misery (novel). --- Morality. --- Narration. --- Narrative structure. --- Narrative. --- Newgate novel. --- Novel. --- Novelist. --- Oxford University Press. --- Parody. --- Paul Clifford. --- Phenomenon. --- Philosopher. --- Philosophy. --- Poetry. --- Political philosophy. --- Practical reason. --- Probability. --- Prose. --- Publication. --- Quantity. --- Reason. --- Ridicule. --- Roland Barthes. --- Rookwood (novel). --- Sensation novel. --- Steven Marcus. --- Subplot. --- Suggestion. --- Teleology. --- The Intuitionist. --- The Life and Opinions of Tristram Shandy, Gentleman. --- The Marriage Plot. --- The Other Hand. --- The Pickwick Papers. --- Theft. --- Theory. --- Thought. --- Usage. --- Utilitarianism. --- Victorian literature. --- William Harrison Ainsworth. --- William Whewell. --- Writer. --- Writing.
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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.
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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