Main Category: Mathematics >> Sub Category: Geometry
Foundations of Differential Geometry

Contents: Differentiable Manifolds; Submersions and Immersions; Vector Fields and Flows; Lie Groups; Vector Bundles; Differential Forms; Integration on Manifolds; De Rham cohomology; Cohomology with compact supports and Poincare duality; De Rham cohomology of compact manifolds; Derivations on the Algebra of Differential Forms; Fiber Bundles and Connections; Principal Fiber Bundles and G-Bundles; Principal and Induced Connections; Characteristic classes; Jets.     

Author Name :Peter W. Michor

No Of Visit :617      Posted Comments :

An Introduction to Complex Algebraic Geometry

The material presented here consists of a more or less self-contained advanced course in complex algebraic geometry presupposing only some familiarity with the theory of algebraic curves or Riemann surfaces. But the goal, as in the lectures, is to understand the Enriques classification of surfaces from the point of view of Mori-theory.     

Author Name :Chris Peters

No Of Visit :614      Posted Comments :

Geometric Methods in the Algebraic Theory of Quadratic Forms

The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes an introduction to motives of quadrics by A. Vishik, with various applications, notably to the splitting patterns of quadratic forms, papers by O. Izhboldin and N. Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields withu-invariant 9, and a contribution in French by B. Kahn which lays out a general framework for the computation of the unramified cohomology groups of quadrics and other cellular varieties.     

Author Name :Oleg T. Izhboldin, Bruno Kahn, Nikita A. Karpenko, Alexander Vishik

No Of Visit :560      Posted Comments :

Geometric Methods in the Algebraic Theory of Quadratic Forms

The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadricshave beencentral to the proofs of fundamental results since the renewal of the theory by Pfister in the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems.     

Author Name :Oleg T. Izhboldin, Bruno Kahn, Nikita A. Karpenko, Alexander Vishik

No Of Visit :830      Posted Comments :

The Geometry of Physics

Theodore Frankel explains those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms essential to a better understanding of classical and modern physics and engineering. Key highlights of his new edition are the inclusion of three new appendices that cover symmetries, quarks, and meson masses; representations and hyperelastic bodies; and orbits and Morse-Bott Theory in compact Lie groups. Geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space.     

Author Name :Theodore Frankel

No Of Visit :598      Posted Comments :

Handbook of Algebraic Topology

Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.     

Author Name :I.M. James

No Of Visit :450      Posted Comments :

Applied Differential Geometry

This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples     

Author Name :William L. Burke

No Of Visit :450      Posted Comments :

Noncommutative Geometry

This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.     

Author Name :Alain Connes

No Of Visit :437      Posted Comments :

A Basic Course in Algebraic Topology

This book is intended to serve as a textbook for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind the various concepts is emphasized. The text consists of material from the first five chapters of the author's earlier book, ALGEBRAIC TOPOLOGY: AN INTRODUCTION (GTM 56), together with almost all of the now out-of- print SINGULAR HOMOLOGY THEORY (GTM 70). The material from the earlier books has been carefully revised, corrected, and brought up to date.     

Author Name :William S. Massey

No Of Visit :440      Posted Comments :

Lectures on Differential Geometry

This is a translation of an introductory text based on a lecture series delivered by the renowned differential geometer, Professor S.S. Chern in Beijing University in 1980. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, sought to combine simplicity and economy of approach with depth of contents. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fibre bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds (with a succinct introduction to the theory of Chern classes), and an appendix on the relationship between differential geometry and theoretical physics, this book includes a new chapter on Finsler geometry and a new appendix on the history and recent developments of differential geometry, the latter prepared specifically for this edition by Professor Chern to bring the text into perspective.     

Author Name :S. S. Chern, W. H. Chen, K. S. Lam

No Of Visit :464      Posted Comments :

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