K-Theory

Released on by Max Karoubi
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  • K-Theory Book Detail

  • Author : Max Karoubi
  • Release Date : 2009-11-27
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 337
  • ISBN 13 : 3540798900
  • File Size : 39,39 MB
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K-Theory by Max Karoubi PDF Summary

Book Description: From the Preface: K-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem. For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch considered a topological analog defined for any compact space X, a group K{X) constructed from the category of vector bundles on X. It is this ''topological K-theory" that this book will study. Topological K-theory has become an important tool in topology. Using K- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are S1, S3 and S7. Moreover, it is possible to derive a substantial part of stable homotopy theory from K-theory. The purpose of this book is to provide advanced students and mathematicians in other fields with the fundamental material in this subject. In addition, several applications of the type described above are included. In general we have tried to make this book self-contained, beginning with elementary concepts wherever possible; however, we assume that the reader is familiar with the basic definitions of homotopy theory: homotopy classes of maps and homotopy groups.Thus this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".

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K-Theory

K-Theory

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From the Preface: K-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem. For each projective algebraic variety, Grothendiec

The $K$-book

The $K$-book

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Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vec

Topology and K-Theory

Topology and K-Theory

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These are notes from a graduate student course on algebraic topology and K-theory given by Daniel Quillen at the Massachusetts Institute of Technology during 19

Complex Topological K-Theory

Complex Topological K-Theory

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Topological K-theory is a key tool in topology, differential geometry and index theory, yet this is the first contemporary introduction for graduate students ne

K-theory

K-theory

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These notes are based on the course of lectures I gave at Harvard in the fall of 1964. They constitute a self-contained account of vector bundles and K-theory a