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The K-Book: An Introduction to Algebraic K-theory (Graduate Studies in Mathematics, 145) - Hardcover
Synopsis
Algebraic K-theory is a field of abstract algebra concerning projective modules over a ring and vector bundles over schemes. It has many applications in mathematics such as algebraic topology and geometry, number theory and operator theory. In advanced physics there are applications such as string theory, D-brane theory and condensed matter physics. In this graduate level textbook Weibel presents the reader with a detailed overview of the field. Topics include Chern classes, Picard groups, Algebraic vector bundles, basic as well as more complex constructions of K0 and K1, as well as higher order K-groups Kn. There are many exercises at the end of each chapter and rigorous proofs throughout. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com)
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About the Author
Charles A. Weibel , Rutgers University, New Brunswick, NJ, USA
Review
Weibel presents his important and elegant subject with the authority of an experienced insider, placing stresses where they should be, presenting motivations and characterizations (always succinctly) so as to familiarize the reader with the shape of the subject. ... it contains a great number of examples, woven beautifully into the narrative, and excellent exercises. --Mathematical Association of America
Charles Weibel's 'K-book' offers a plethora of material from both classical and more recent algebraic K-theory. It is a perfect source book for seasoned graduate students and working researchers who are willing and eager to follow the author's expository path and who are ready for a lot of additional reading and self-reliant work. The many instructive examples and clarifying remarks help the reader grasp the essentials of algebraic K-theory from a panoramic view, and the entire exposition represents a highly valuable and useful guide to the subject in all its diversity and topicality. Although barely being a textbook or neophyte in the field, despite the wealth of background material sketched wherever necessary, the book, under review, is certainly the most topical presentation of algebraic K-theory at this time and an excellent enhancement of the existing literature in any case. --Newsletter of the European Mathematical Society
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- PublisherAmer Mathematical Society
- Publication date2013
- ISBN 10 0821891324
- ISBN 13 9780821891322
- BindingHardcover
- LanguageEnglish
- Number of pages618
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K-Book : An Introduction to Algebraic K-theory
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Gebunden. Condition: New. KlappentextrnrnInformally, 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. Seller Inventory # 595068227
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Buch. Condition: Neu. Neuware - 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 algebraic and geometric questions. Algebraic $K$-theory, which is the main character of this book, deals mainly with studying the structure of rings. However, it turns out that even working in a purely algebraic context, one requires techniques from homotopy theory to construct the higher $K$-groups and to perform computations. Seller Inventory # 9780821891322
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