Basic Bundle Theory and K-Cohomology Invariants PDF Download

Author: Dale Husemöller
Publisher: Springer Science & Business Media
ISBN: 3540749551
Category : Mathematics
Languages : en
Pages : 344

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Book Description
Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory. It aims to provide newcomers to the field with solid foundations in topological K-theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object. One renewed motivation for studying this subject, comes from quantum field theory, where topological invariants play an important role.

Author: Steven Dale Cutkosky
Publisher: American Mathematical Soc.
ISBN: 0821832646
Category : Mathematics
Languages : en
Pages : 258

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Book Description
This volume contains 13 papers from the conference on ``Hilbert Schemes, Vector Bundles and Their Interplay with Representation Theory''. The papers are written by leading mathematicians in algebraic geometry and representation theory and present the latest developments in the field. Among other contributions, the volume includes several very impressive and elegant theorems in representation theory by R. Friedman and J. W. Morgan, convolution on homology groups of moduli spaces of sheaves on K3 surfaces by H. Nakajima, and computation of the $S1$ fixed points in Quot-schemes and mirror principle computations for Grassmanians by S.-T. Yau, et al. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, topology and their applications to high energy physics.

Author: N. J. Hitchin
Publisher: Cambridge University Press
ISBN: 0521498783
Category : Mathematics
Languages : en
Pages : 359

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Book Description
This book is a collection of survey articles by the main speakers at the 1993 Durham symposium on vector bundles in algebraic geometry.

Author: Jerzy Weyman
Publisher: Cambridge University Press
ISBN: 9780521621977
Category : Mathematics
Languages : en
Pages : 404

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Book Description
The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method.

Author: Gert-Martin Greuel
Publisher: Springer
ISBN: 3540478515
Category : Mathematics
Languages : en
Pages : 396

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Book Description
It is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction. These relations however cannot be considered to be either completely understood or fully exploited. These proceedings document recent developments in the area. The questions and methods of representation theory have applications to singularities and to vector bundles. Representation theory itself, which had primarily developed its methods for Artinian algebras, starts to investigate algebras of higher dimension partly because of these applications. Future research in representation theory may be spurred by the classification of singularities and the highly developed theory of moduli for vector bundles. The volume contains 3 survey articles on the 3 main topics mentioned, stressing their interrelationships, as well as original research papers.

Author: T. Tom Dieck
Publisher: Springer
ISBN: 3540385177
Category : Mathematics
Languages : en
Pages : 317

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Book Description

Author: Shoshichi Kobayashi
Publisher: Princeton University Press
ISBN: 1400858682
Category : Mathematics
Languages : en
Pages : 317

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Book Description
Holomorphic vector bundles have become objects of interest not only to algebraic and differential geometers and complex analysts but also to low dimensional topologists and mathematical physicists working on gauge theory. This book, which grew out of the author's lectures and seminars in Berkeley and Japan, is written for researchers and graduate students in these various fields of mathematics. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author: Steve Bradlow
Publisher: Cambridge University Press
ISBN: 0521734711
Category : Mathematics
Languages : en
Pages : 516

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Book Description
Coverage includes foundational material as well as current research, authored by top specialists within their fields.

Author: A. N. Rudakov
Publisher: Cambridge University Press
ISBN: 0521388112
Category : Mathematics
Languages : en
Pages : 153

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Book Description
Arising out of a series of seminars organized in Moscow by A.N. Rudakov, this volume is devoted to the use of helices as a method for studying exceptional vector bundles, an important and natural concept in algebraic geometry.

Author: Ryoshi Hotta
Publisher: Springer Science & Business Media
ISBN: 081764363X
Category : Mathematics
Languages : en
Pages : 408

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Book Description
D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.