{"product_id":"homology-of-linear-groups-concise-reference-for-k-theory","title":"Homology of Linear Groups - Concise Reference for K-Theory","description":"\u003cp\u003eIn this review the book Homology of Linear Groups is recommended for graduate students and researchers who need a focused reference on the homological methods behind algebraic K-theory. The text collects foundational results from Quillen through later work by Suslin and van der Kallen, and the single biggest reason to buy is its concentration of proofs and stability theorems that are otherwise scattered across original papers. Readers will find a tightly organized account that emphasizes the calculation of group homology and its role in higher K-groups.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eHistorical development:\u003c\/strong\u003e Traces the theory from Quillen's calculation of the cohomology of GLn(Fq) to later contributions, helping readers follow the subject's progression.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eStability theorems:\u003c\/strong\u003e Presents the stability results of Suslin and van der Kallen so readers can apply them directly in computations of homology of matrix groups.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eLow-dimensional results:\u003c\/strong\u003e Collects concrete low-dimensional calculations that are useful for hands-on work in K-theory and group cohomology.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eRank one groups:\u003c\/strong\u003e Includes recent results for rank one groups, offering up-to-date perspectives not commonly found in a single volume.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eFriedlander-Milnor discussion:\u003c\/strong\u003e A dedicated chapter explains the Friedlander-Milnor conjecture and its implications for treating algebraic groups as discrete groups.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThe book is aimed at graduate students, researchers and practitioners in \u003cstrong\u003eK-theory\u003c\/strong\u003e, algebraic geometry, topology and group cohomology who require a concise reference that gathers important theorems and computations in one place. It is particularly helpful for those working on the homology of GLn, applications to algebraic K-groups, or following the development of stability techniques.\u003c\/p\u003e\n\u003cp\u003eThose looking for elementary introductions or broad surveys of algebra may want a more introductory text, since this volume expects familiarity with group cohomology and algebraic groups and focuses on assembling and explaining specific advanced results.\u003c\/p\u003e\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eWell organized collection of foundational results from Quillen through later contributors for easy reference.\u003c\/li\u003e\n\u003cli\u003eIncludes stability theorems and low-dimensional computations that facilitate practical work in K-theory.\u003c\/li\u003e\n\u003cli\u003eThe Friedlander-Milnor chapter offers a clear presentation of a significant conjecture and its context.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eNot an introductory textbook; readers without background in group cohomology may find it terse.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eHomology of Linear Groups (Progress in Mathematics)\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthor\u003c\/td\u003e\n\u003ctd\u003eKevin P. P. Knudson\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSubject focus\u003c\/td\u003e\n\u003ctd\u003eHomology of matrix groups and algebraic K-theory\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIncludes\u003c\/td\u003e\n\u003ctd\u003eStability theorems, low-dimensional results, rank one groups\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eNotable chapter\u003c\/td\u003e\n\u003ctd\u003eFriedlander-Milnor conjecture on discrete algebraic groups\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIntended audience\u003c\/td\u003e\n\u003ctd\u003eGraduate students and researchers in mathematics\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eThis volume is a compact, authoritative reference for specialists who need theorems and proofs about the homology of linear groups collected in one place. It is good value for researchers and advanced students working on algebraic K-theory or group cohomology, but it is not a substitute for an introductory text on the subject.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eDoes this book cover Quillen's work?\u003c\/strong\u003e\u003cbr\u003eYes, it traces the development beginning with Quillen's calculation of the cohomology of GLn(Fq) and explains its importance for higher algebraic K-groups.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eIs this suitable for beginners?\u003c\/strong\u003e\u003cbr\u003eNo, the book assumes familiarity with group cohomology and algebraic groups and is aimed at graduate-level readers and researchers.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eDoes it include recent results?\u003c\/strong\u003e\u003cbr\u003eYes, it presents later results including stability theorems and recent work on rank one groups alongside classical material.\u003c\/p\u003e","brand":"Kevin P. 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