The K-Book: An Introduction to Algebraic K-Theory (Graduate Studies in Mathematics)

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9780821891322: The K-Book: An Introduction to Algebraic K-Theory (Graduate Studies in Mathematics)

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. The resulting interplay of algebra, geometry, and topology in K-theory provides a fascinating glimpse of the unity of mathematics. This book is a comprehensive introduction to the subject of algebraic K-theory. It blends classical algebraic techniques for K0 and K1 with newer topological techniques for higher K-theory such as homotopy theory, spectra, and cohomological descent. The book takes the reader from the basics of the subject to the state of the art, including the calculation of the higher K-theory of number fields and the relation to the Riemann zeta function.

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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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Weibel, Charles A (Rutgers University, New Jersey)
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ISBN 10: 0821891324 ISBN 13: 9780821891322
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Descrizione libro American Mathematical Society, 2013. Condizione libro: New. 2013. Hardcover. Series: Graduate Studies in Mathematics. Num Pages: 642 pages. BIC Classification: PBF. Category: (G) General (US: Trade). Dimension: 257 x 185 x 36. Weight in Grams: 1242. . . . . . . Codice libro della libreria V9780821891322

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Descrizione libro American Mathematical Society. Microfilm. Condizione libro: new. BRAND NEW, The K-Book: An Introduction to Algebraic K-Theory, Charles A. Weibel, 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. The resulting interplay of algebra, geometry, and topology in $K$-theory provides a fascinating glimpse of the unity of mathematics. This book is a comprehensive introduction to the subject of algebraic $K$-theory. It blends classical algebraic techniques for $K_0$ and $K_1$ with newer topological techniques for higher $K$-theory such as homotopy theory, spectra, and cohomological descent. The book takes the reader from the basics of the subject to the state of the art, including the calculation of the higher $K$-theory of number fields and the relation to the Riemann zeta function. Codice libro della libreria B9780821891322

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Descrizione libro American Mathematical Society, United States, 2013. Microfilm. Condizione libro: New. Language: English . Brand New Book. 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. The resulting interplay of algebra, geometry, and topology in $K$-theory provides a fascinating glimpse of the unity of mathematics. This book is a comprehensive introduction to the subject of algebraic $K$-theory. It blends classical algebraic techniques for $K 0$ and $K 1$ with newer topological techniques for higher $K$-theory such as homotopy theory, spectra, and cohomological descent. The book takes the reader from the basics of the subject to the state of the art, including the calculation of the higher $K$-theory of number fields and the relation to the Riemann zeta function. Codice libro della libreria AAU9780821891322

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Descrizione libro American Mathematical Society. Condizione libro: New. 2013. Hardcover. Series: Graduate Studies in Mathematics. Num Pages: 642 pages. BIC Classification: PBF. Category: (G) General (US: Trade). Dimension: 257 x 185 x 36. Weight in Grams: 1242. . . . . . Books ship from the US and Ireland. Codice libro della libreria V9780821891322

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Descrizione libro American Mathematical Society, 2013. Condizione libro: New. book. Codice libro della libreria ria9780821891322_rkm

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Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97808218913220000000

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Descrizione libro American Mathematical Society, United States, 2013. Microfilm. Condizione libro: New. Language: English . Brand New Book. 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. The resulting interplay of algebra, geometry, and topology in $K$-theory provides a fascinating glimpse of the unity of mathematics. This book is a comprehensive introduction to the subject of algebraic $K$-theory. It blends classical algebraic techniques for $K 0$ and $K 1$ with newer topological techniques for higher $K$-theory such as homotopy theory, spectra, and cohomological descent. The book takes the reader from the basics of the subject to the state of the art, including the calculation of the higher $K$-theory of number fields and the relation to the Riemann zeta function. Codice libro della libreria AAU9780821891322

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Descrizione libro American Mathematical Society, 2013. Hardcover. Condizione libro: New. book. Codice libro della libreria 0821891324

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Descrizione libro American Mathematical Society, 2013. Condizione libro: New. Codice libro della libreria EH9780821891322

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