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Product Identifiers
PublisherAmerican Mathematical Society
ISBN-100821891324
ISBN-139780821891322
eBay Product ID (ePID)229506385
Product Key Features
Number of Pages618 Pages
Publication NameK-Book : an Introduction to Algebraic K-Theory
LanguageEnglish
Publication Year2013
SubjectTopology
TypeTextbook
AuthorCharles A. Weibel
Subject AreaMathematics
SeriesGraduate Studies in Mathematics Ser.
FormatHardcover
Dimensions
Item Height1.5 in
Item Weight43.7 Oz
Item Length10.3 in
Item Width7.4 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2012-039660
Dewey Edition23
TitleLeadingThe
Reviews"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." -- MAA
Series Volume Number145
Dewey Decimal512/.66
Table Of ContentProjective modules and vector bundles The Grothendieck group $K_0$ $K_1$ and $K_2$ of a ring Definitions of higher $K$-theory The fundamental theorems of higher $K$-theory The higher $K$-theory of fields Nomenclature Bibliography Index
SynopsisInformally, 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., 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.
LC Classification NumberQA612.33.W45 2013
