The $K$-book - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The $K$-book write by Charles A. Weibel. This book was released on 2013-06-13. The $K$-book available in PDF, EPUB and Kindle. 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 vector spaces and producing important intrinsic invariants which are useful in the study of algebr
K-Theory
K-Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook K-Theory write by Max Karoubi. This book was released on 2009-11-27. K-Theory available in PDF, EPUB and Kindle. 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".
Algebraic K-Theory and Its Applications
Algebraic K-Theory and Its Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic K-Theory and Its Applications write by Jonathan Rosenberg. This book was released on 2012-12-06. Algebraic K-Theory and Its Applications available in PDF, EPUB and Kindle. Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.
An Algebraic Introduction to K-Theory
An Algebraic Introduction to K-Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Algebraic Introduction to K-Theory write by Bruce A. Magurn. This book was released on 2002-05-20. An Algebraic Introduction to K-Theory available in PDF, EPUB and Kindle. This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra (including Galois theory and modules over a principal ideal domain). The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. No experience with analysis, geometry, number theory or topology is assumed. Within the context of linear algebra, K-theory organises and clarifies the relations among ideal class groups, group representations, quadratic forms, dimensions of a ring, determinants, quadratic reciprocity and Brauer groups of fields. By including introductions to standard algebra topics (tensor products, localisation, Jacobson radical, chain conditions, Dedekind domains, semi-simple rings, exterior algebras), the author makes algebraic K-theory accessible to first-year graduate students and other mathematically sophisticated readers. Even if your algebra is rusty, you can read this book; the necessary background is here, with proofs.
Algebraic K-Theory
Algebraic K-Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic K-Theory write by Richard G. Swan. This book was released on 2006-11-14. Algebraic K-Theory available in PDF, EPUB and Kindle. From the Introduction: "These notes are taken from a course on algebraic K-theory [given] at the University of Chicago in 1967. They also include some material from an earlier course on abelian categories, elaborating certain parts of Gabriel's thesis. The results on K-theory are mostly of a very general nature."
