{"product_id":"cyclic-homology-grundlehren-der-mathematischen-wissenschaften","title":"Cyclic Homology (Grundlehren der mathematischen Wissenschaften)","description":"\u003cp\u003eOur review of Cyclic Homology notes it is a specialist graduate-level text aimed at researchers and advanced students in algebra and homological methods. The second edition adds a new chapter that bridges earlier material to broader algebraic K-theory topics, making this volume especially valuable for readers seeking a rigorous comparison between MacLane (co)homology and stable K-theory. Overall, the book is worth acquiring for its clear transition material and the construction using derived functors over polynomial functors that underpins the isomorphism claim.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eNew chapter on MacLane (co)homology:\u003c\/strong\u003e Presents a focused development comparing MacLane (co)homology with a variant of algebraic K-theory known as stable K-theory, useful for specialists following recent theoretical links.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eIsomorphism result:\u003c\/strong\u003e Explains why MacLane (co)homology and stable K-theory turn out to be isomorphic, providing a concise statement of the main comparison for researchers to reference.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eDerived functors approach:\u003c\/strong\u003e Uses a third theory constructed from derived functors over the category of polynomial functors as the main technical tool, giving readers explicit homological machinery.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eTransition material:\u003c\/strong\u003e Chapter 13 acts as a bridge from the first 12 chapters, helping readers move from foundational cyclic homology topics to more advanced K-theoretic comparisons.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eSecond edition updates:\u003c\/strong\u003e Incorporates new content that refines and extends the original exposition, making it the recommended edition for current study.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThe book targets graduate students, postdocs, and established researchers in pure mathematics with a focus on algebra, homological algebra, and algebraic K-theory who need a rigorous reference that connects cyclic homology to related cohomological theories. It is best used as a course text for advanced seminars or as a companion reference when working through research that intersects MacLane (co)homology and stable K-theory.\u003c\/p\u003e\n\u003cp\u003eThose without solid background in homological methods or polynomial functors may find the material dense; undergraduate students or casual readers looking for an introductory treatment of homology theories should look for more elementary texts before tackling this volume.\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\u003eConsolidates a technical comparison between MacLane (co)homology and stable K-theory in one accessible chapter.\u003c\/li\u003e\n\u003cli\u003eProvides a clear construction using derived functors that researchers can apply in related contexts.\u003c\/li\u003e\n\u003cli\u003eActs as an effective bridge from foundational cyclic homology to advanced K-theoretic topics.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eMaterial is specialized and assumes significant background, which limits accessibility for non-experts.\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\u003eCyclic Homology (Grundlehren der mathematischen Wissenschaften)\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eEdition\u003c\/td\u003e\n\u003ctd\u003e2nd edition\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthor \/ Brand\u003c\/td\u003e\n\u003ctd\u003eJean-Louis Loday\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eNew content\u003c\/td\u003e\n\u003ctd\u003eChapter 13 on MacLane (co)homology and comparison to stable K-theory\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eMain tool\u003c\/td\u003e\n\u003ctd\u003eDerived functors over the category of polynomial functors\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eScope\u003c\/td\u003e\n\u003ctd\u003eTransition from first 12 chapters to K-theoretic comparisons\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eCyclic Homology second edition is a strong, narrowly focused reference for specialists who need a rigorous comparison between MacLane (co)homology and stable K-theory; its derived functors construction and the new chapter make it good value for advanced students and researchers despite its specialist level.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eDoes this edition include new material?\u003c\/strong\u003e\u003cbr\u003eThe second edition adds chapter 13, comparing MacLane (co)homology with stable K-theory and introducing the derived functors approach used in the comparison.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eIs prior knowledge required?\u003c\/strong\u003e\u003cbr\u003eYes; readers should have a solid background in homological algebra and familiarity with polynomial functors to get the most from the new chapter and comparisons.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eWho benefits most from this book?\u003c\/strong\u003e\u003cbr\u003eGraduate students, postdocs, and researchers working in algebra and algebraic K-theory will gain the most from the rigorous constructions and the bridge material provided.\u003c\/p\u003e","brand":"Jean-Louis Loday","offers":[{"title":"Default Title","offer_id":48245288927451,"sku":"3642083161","price":126.63,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/51jdj9W-GtL._SL1300.jpg?v=1770964550","url":"https:\/\/gearmusthave.com\/products\/cyclic-homology-grundlehren-der-mathematischen-wissenschaften","provider":"GearMustHave","version":"1.0","type":"link"}