Topological Methods in Algebraic Geometry
Author: Friedrich Hirzebruch
Publisher: Springer
Published: 2013-11-11
Total Pages: 241
ISBN-13: 3662306972
DOWNLOAD EBOOK →Author: Friedrich Hirzebruch
Publisher: Springer
Published: 2013-11-11
Total Pages: 241
ISBN-13: 3662306972
DOWNLOAD EBOOK →Author: Friedrich Hirzebruch
Publisher: Ergebnisse der Mathematik Und
Published: 1978
Total Pages: 254
ISBN-13:
DOWNLOAD EBOOK →Author: Friedrich Hirzebruch
Publisher: Springer Science & Business Media
Published: 1995-02-15
Total Pages: 256
ISBN-13: 9783540586630
DOWNLOAD EBOOK →In recent years new topological methods, especially the theory of sheaves founded by J. LERAY, have been applied successfully to algebraic geometry and to the theory of functions of several complex variables. H. CARTAN and J. -P. SERRE have shown how fundamental theorems on holomorphically complete manifolds (STEIN manifolds) can be for mulated in terms of sheaf theory. These theorems imply many facts of function theory because the domains of holomorphy are holomorphically complete. They can also be applied to algebraic geometry because the complement of a hyperplane section of an algebraic manifold is holo morphically complete. J. -P. SERRE has obtained important results on algebraic manifolds by these and other methods. Recently many of his results have been proved for algebraic varieties defined over a field of arbitrary characteristic. K. KODAIRA and D. C. SPENCER have also applied sheaf theory to algebraic geometry with great success. Their methods differ from those of SERRE in that they use techniques from differential geometry (harmonic integrals etc. ) but do not make any use of the theory of STEIN manifolds. M. F. ATIYAH and W. V. D. HODGE have dealt successfully with problems on integrals of the second kind on algebraic manifolds with the help of sheaf theory. I was able to work together with K. KODAIRA and D. C. SPENCER during a stay at the Institute for Advanced Study at Princeton from 1952 to 1954.
Author: Friedrich Hirzebruch
Publisher: Springer
Published: 1978-09-01
Total Pages: 234
ISBN-13: 9783540035251
DOWNLOAD EBOOK →In recent years new topological methods, especially the theory of sheaves founded by J. LERAY, have been applied successfully to algebraic geometry and to the theory of functions of several complex variables. H. CARTAN and J. -P. SERRE have shown how fundamental theorems on holomorphically complete manifolds (STEIN manifolds) can be for mulated in terms of sheaf theory. These theorems imply many facts of function theory because the domains of holomorphy are holomorphically complete. They can also be applied to algebraic geometry because the complement of a hyperplane section of an algebraic manifold is holo morphically complete. J. -P. SERRE has obtained important results on algebraic manifolds by these and other methods. Recently many of his results have been proved for algebraic varieties defined over a field of arbitrary characteristic. K. KODAIRA and D. C. SPENCER have also applied sheaf theory to algebraic geometry with great success. Their methods differ from those of SERRE in that they use techniques from differential geometry (harmonic integrals etc. ) but do not make any use of the theory of STEIN manifolds. M. F. ATIYAH and W. V. D. HODGE have dealt successfully with problems on integrals of the second kind on algebraic manifolds with the help of sheaf theory. I was able to work together with K. KODAIRA and D. C. SPENCER during a stay at the Institute for Advanced Study at Princeton from 1952 to 1954.
Author: G. Giachetta
Publisher: World Scientific
Published: 2005
Total Pages: 715
ISBN-13: 9812701265
DOWNLOAD EBOOK →In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry''s geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.
Author: Jiri Matousek
Publisher: Springer Science & Business Media
Published: 2008-01-12
Total Pages: 221
ISBN-13: 3540766499
DOWNLOAD EBOOK →To the uninitiated, algebraic topology might seem fiendishly complex, but its utility is beyond doubt. This brilliant exposition goes back to basics to explain how the subject has been used to further our understanding in some key areas. A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. This book is the first textbook treatment of a significant part of these results. It focuses on so-called equivariant methods, based on the Borsuk-Ulam theorem and its generalizations. The topological tools are intentionally kept on a very elementary level. No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained.
Author: Edwin H. Spanier
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 502
ISBN-13: 1468493221
DOWNLOAD EBOOK →This book surveys the fundamental ideas of algebraic topology. The first part covers the fundamental group, its definition and application in the study of covering spaces. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds. The final part is devoted to Homotropy theory, including basic facts about homotropy groups and applications to obstruction theory.
Author: B. A. Dubrovin
Publisher:
Published: 2003
Total Pages: 160
ISBN-13: 9780415299190
DOWNLOAD EBOOK →This volume is a classic survey of algebraic geometry and topological methods in various problems of mathematical physics and provides an excellent reference text for graduate students and researchers. The book is divided into three sections: the first part concerns Hamiltonian formalism and methods that generalise Morse for certain dynamical systems of physical origin; the second part presents algebraic geometry analysis of the Yang-Baxter equations for two dimensional models; part three presents the theory of multidimensional theta functions of Abel, Riemann, Poincare in a form that is elementary and convenient for applications.
Author: Hernan Ocampo
Publisher: Cambridge University Press
Published: 2010-04-29
Total Pages: 435
ISBN-13: 113948673X
DOWNLOAD EBOOK →Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest.
Author: Vladimir I. Arnold
Publisher: Springer Science & Business Media
Published: 2008-01-08
Total Pages: 376
ISBN-13: 0387225897
DOWNLOAD EBOOK →The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.