Download Full eBooks in PDF
Connections Curvature And Cohomology Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Connections Curvature And Cohomology book. This book definitely worth reading, it is an incredibly well-written.
Author : Anonim
Publisher : Academic Press
Page : 442 pages
File Size : 42,9 Mb
Release : 1972-07-31
Category : Mathematics
ISBN : 008087360X
Connections, Curvature, and Cohomology V1
Author : Werner Hildbert Greub,Stephen Halperin,Ray Vanstone
Publisher : Academic Press
Page : 618 pages
File Size : 51,8 Mb
Release : 1972
Category : Mathematics
ISBN : 9780123027030
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.
Author : Werner Greub
Publisher : Academic Press
Page : 617 pages
File Size : 46,6 Mb
Release : 1976-02-19
Category : Mathematics
ISBN : 9780080879277
Connections, Curvature, and Cohomology Volume 3
Author : Werner Hildbert Greub,Stephen Halperin,Ray Vanstone
Publisher : Unknown
Page : 572 pages
File Size : 53,7 Mb
Release : 1973
Category : Mathematics
ISBN : UOM:39015038846427
Volume 2.
Author : Loring W. Tu
Publisher : Springer
Page : 347 pages
File Size : 45,6 Mb
Release : 2017-06-01
Category : Mathematics
ISBN : 9783319550848
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.
Author : Ib H. Madsen,Jxrgen Tornehave
Publisher : Cambridge University Press
Page : 302 pages
File Size : 52,9 Mb
Release : 1997-03-13
Category : Mathematics
ISBN : 0521589568
An introductory textbook on cohomology and curvature with emphasis on applications.
Author : Anonim
Publisher : Academic Press
Page : 314 pages
File Size : 49,8 Mb
Release : 2011-08-29
Category : Mathematics
ISBN : 0080873235
Curvature and Homology
Author : J.L. Dupont
Publisher : Springer
Page : 185 pages
File Size : 49,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540359142
Author : Vyacheslav L. Girko
Publisher : Academic Press
Page : 568 pages
File Size : 52,8 Mb
Release : 2016-08-23
Category : Computers
ISBN : 9780080873619
Spectral Theory of Random Matrices
Author : Raoul Bott,Loring W. Tu
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 45,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475739510
Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.
Author : John Willard Milnor,James D. Stasheff
Publisher : Princeton University Press
Page : 342 pages
File Size : 51,5 Mb
Release : 1974
Category : Mathematics
ISBN : 0691081220
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.
Author : Ib H. Madsen,Jxrgen Tornehave
Publisher : Cambridge University Press
Page : 294 pages
File Size : 45,7 Mb
Release : 1997-03-13
Category : Mathematics
ISBN : 0521580595
De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of characteristic classes from the curvature point of view. It requires no prior knowledge of the concepts of algebraic topology or cohomology. The first ten chapters study cohomology of open sets in Euclidean space, treat smooth manifolds and their cohomology and end with integration on manifolds. The last eleven chapters cover Morse theory, index of vector fields, Poincaré duality, vector bundles, connections and curvature, Chern and Euler classes, Thom isomorphism, and the general Gauss-Bonnet theorem. The text includes over 150 exercises, and gives the background necessary for the modern developments in gauge theory and geometry in four dimensions, but it also serves as an introductory course in algebraic topology. It will be invaluable to anyone who wishes to know about cohomology, curvature, and their applications.
Author : Clifford Henry Taubes
Publisher : OUP Oxford
Page : 313 pages
File Size : 51,7 Mb
Release : 2011-10-13
Category : Mathematics
ISBN : 9780191621222
Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects. Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. Other material covered includes the basic theorems about geodesics and Jacobi fields, the classification theorem for flat connections, the definition of characteristic classes, and also an introduction to complex and Kähler geometry. Differential Geometry uses many of the classical examples from, and applications of, the subjects it covers, in particular those where closed form expressions are available, to bring abstract ideas to life. Helpfully, proofs are offered for almost all assertions throughout. All of the introductory material is presented in full and this is the only such source with the classical examples presented in detail.
Author : Ib Henning Madsen,Jørgen Tornehave
Publisher : Unknown
Page : 286 pages
File Size : 53,9 Mb
Release : 1997
Category : Characteristic classes
ISBN : 7302075638
Author : Werner Ballmann
Publisher : Birkhäuser
Page : 169 pages
File Size : 47,7 Mb
Release : 2018-07-18
Category : Mathematics
ISBN : 9783034809832
This book provides an introduction to topology, differential topology, and differential geometry. It is based on manuscripts refined through use in a variety of lecture courses. The first chapter covers elementary results and concepts from point-set topology. An exception is the Jordan Curve Theorem, which is proved for polygonal paths and is intended to give students a first glimpse into the nature of deeper topological problems. The second chapter of the book introduces manifolds and Lie groups, and examines a wide assortment of examples. Further discussion explores tangent bundles, vector bundles, differentials, vector fields, and Lie brackets of vector fields. This discussion is deepened and expanded in the third chapter, which introduces the de Rham cohomology and the oriented integral and gives proofs of the Brouwer Fixed-Point Theorem, the Jordan-Brouwer Separation Theorem, and Stokes's integral formula. The fourth and final chapter is devoted to the fundamentals of differential geometry and traces the development of ideas from curves to submanifolds of Euclidean spaces. Along the way, the book discusses connections and curvature--the central concepts of differential geometry. The discussion culminates with the Gauß equations and the version of Gauß's theorema egregium for submanifolds of arbitrary dimension and codimension. This book is primarily aimed at advanced undergraduates in mathematics and physics and is intended as the template for a one- or two-semester bachelor's course.