Download or read book Connections Curvature and Cohomology V1 written by and published by Academic Press. This book was released on 1972-07-31 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Connections, Curvature, and Cohomology V1

Download or read book Connections Curvature and Cohomology written by Werner Hildbert Greub and published by Academic Press. This book was released on 1972 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph developed out of the Abendseminar of 1958-1959 at the University of Zürich. The purpose of this monograph is to develop the de Rham cohomology theory, and to apply it to obtain topological invariants of smooth manifolds and fibre bundles. It also addresses the purely algebraic theory of the operation of a Lie algebra in a graded differential algebra.

Download or read book Connections Curvature and Cohomology Volume 3 written by Werner Greub and published by Academic Press. This book was released on 1976-02-19 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: Connections, Curvature, and Cohomology Volume 3

Download or read book Algebraic Models in Geometry written by Yves Félix and published by OUP Oxford. This book was released on 2008-03-13 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rational homotopy is a very powerful tool for differential topology and geometry. This text aims to provide graduates and researchers with the tools necessary for the use of rational homotopy in geometry. Algebraic Models in Geometry has been written for topologists who are drawn to geometrical problems amenable to topological methods and also for geometers who are faced with problems requiring topological approaches and thus need a simple and concrete introduction to rational homotopy. This is essentially a book of applications. Geodesics, curvature, embeddings of manifolds, blow-ups, complex and Kähler manifolds, symplectic geometry, torus actions, configurations and arrangements are all covered. The chapters related to these subjects act as an introduction to the topic, a survey, and a guide to the literature. But no matter what the particular subject is, the central theme of the book persists; namely, there is a beautiful connection between geometry and rational homotopy which both serves to solve geometric problems and spur the development of topological methods.

Download or read book Collected Works Michael Atiyah Collected WOrks written by Michael Atiyah and published by Oxford University Press. This book was released on 1988-04-28 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of the works of Michael Atiyah, a well-established mathematician and winner of the Fields Medal. It is thematically divided into volumes; this one discusses index theory.

Download or read book Probabilistic Models of Cosmic Backgrounds written by Anatoliy Malyarenko and published by CRC Press. This book was released on 2024-06-30 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining research methods from various areas of mathematics and physics, Probabilistic Models of Cosmic Backgrounds describes the isotropic random sections of certain fibre bundles and their applications to creating rigorous mathematical models of both discovered and hypothetical cosmic backgrounds. Previously scattered and hard-to-find mathematical and physical theories have been assembled from numerous textbooks, monographs, and research papers, and explained from different or even unexpected points of view. This consists of both classical and newly discovered results necessary for understanding a sophisticated problem of modelling cosmic backgrounds. The book contains a comprehensive description of mathematical and physical aspects of cosmic backgrounds with a clear focus on examples and explicit calculations. Its reader will bridge the gap of misunderstanding between the specialists in various theoretical and applied areas who speak different scientific languages. The audience of the book consists of scholars, students, and professional researchers. A scholar will find basic material for starting their own research. A student will use the book as supplementary material for various courses and modules. A professional mathematician will find a description of several physical phenomena at the rigorous mathematical level. A professional physicist will discover mathematical foundations for well-known physical theories.

Download or read book Connections Curvature and Cohomology Lie groups principal bundles and characteristic classes written by Werner Hildbert Greub and published by . This book was released on 1973 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 2.

Download or read book Differential Geometry written by Loring W. Tu and published by Springer. This book was released on 2017-06-01 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included. Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.

Download or read book Loop Spaces Characteristic Classes and Geometric Quantization written by Jean-Luc Brylinski and published by Springer Science & Business Media. This book was released on 2009-12-30 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac’s quantization of the electrical charge.

Download or read book Characteristic Classes written by John Willard Milnor and published by Princeton University Press. This book was released on 1974 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.

Download or read book Book Catalog of the Library and Information Services Division Shelf List catalog written by Environmental Science Information Center. Library and Information Services Division and published by . This book was released on 1977 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book American Book Publishing Record Cumulative 1950 1977 written by R.R. Bowker Company. Department of Bibliography and published by . This book was released on 1978 with total page 2006 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Annales Academiae Scientiarum Fennicae written by and published by . This book was released on 1982 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometry of Differential Forms written by Shigeyuki Morita and published by American Mathematical Soc.. This book was released on 2001 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the times of Gauss, Riemann, and Poincare, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms. The book by Morita is a comprehensive introduction to differential forms. It begins with a quick introduction to the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results concerning them, such as the de Rham and Frobenius theorems. The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and the theory of characteristic classes. Among the less traditional topics treated is a detailed description of the Chern-Weil theory. The book can serve as a textbook for undergraduate students and for graduate students in geometry.

Download or read book Library of Congress Catalog written by Library of Congress and published by . This book was released on 1974-04 with total page 1030 pages. Available in PDF, EPUB and Kindle. Book excerpt: A cumulative list of works represented by Library of Congress printed cards.

Download or read book Subject Catalog written by Library of Congress and published by . This book was released on with total page 1032 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Monographic Series written by Library of Congress and published by . This book was released on with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: