{"product_id":"algebraic-l-theory-and-topological-manifolds-definitive-survey","title":"Algebraic L-theory and Topological Manifolds - Definitive Survey","description":"\u003cp\u003eIn this review of Algebraic L-theory and Topological Manifolds the bottom line is simple: this is the definitive reference for mathematicians working at the intersection of algebraic surgery theory and topological manifolds. Written as a rigorous account, the book identifies manifold structures in homotopy types of Poincare duality spaces via local quadratic structures, and it packages that identification into the algebraic L-theory assembly map. Readers seeking a deep, algebraic formulation of the Novikov conjectures will find the material essential.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eComprehensive treatment:\u003c\/strong\u003e Presents a full account of how algebraic L-theory applies to the surgery classification of topological manifolds, making it a single-source reference.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eCore theorem explained:\u003c\/strong\u003e Identifies manifold structures in a homotopy type with local quadratic structures on the universal cover, clarifying a central conceptual correspondence.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eAssembly map focus:\u003c\/strong\u003e Describes the algebraic L-theory assembly map in detail, showing how local quadratic duality structures pass to global invariants.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eNovikov conjecture formulation:\u003c\/strong\u003e Gives a purely algebraic statement of the Novikov conjectures on higher signatures, demonstrating that other formulations factor through this one.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eTheoretical depth:\u003c\/strong\u003e Emphasizes chain homotopy and fibre identifications that distinguish homotopy types of manifolds from Poincare duality spaces, useful for advanced research.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eGraduate students, researchers, and established mathematicians working in topology, surgery theory, or geometric topology will benefit most from this book. It is tailored to readers who already have familiarity with Poincare duality spaces, chain complexes, and basic surgery techniques and who need a rigorous algebraic framework for classification problems.\u003c\/p\u003e\n\u003cp\u003eThose looking for an introductory or elementary textbook in topology should look elsewhere; this volume assumes significant background and is focused on formal algebraic formulations and research-level results rather than pedagogy for beginners.\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\u003eAuthoritative exposition that consolidates algebraic L-theory applications to manifold classification in one place.\u003c\/li\u003e\n\u003cli\u003eClear identification of the role of the algebraic L-theory assembly map, useful for connecting local and global invariants.\u003c\/li\u003e\n\u003cli\u003eProvides a rigorous algebraic formulation of the Novikov conjectures, giving a clean target for further research.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eSpecialized and technical: not suitable as an introductory text for readers without prior background in algebraic topology or surgery theory.\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\u003eAlgebraic L-theory and Topological Manifolds\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSeries\u003c\/td\u003e\n\u003ctd\u003eCambridge Tracts in Mathematics, Series Number 102\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthor \/ Brand\u003c\/td\u003e\n\u003ctd\u003eA. A. Ranicki\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePrimary focus\u003c\/td\u003e\n\u003ctd\u003eApplications of algebraic L-theory to surgery classification of manifolds\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eCentral result\u003c\/td\u003e\n\u003ctd\u003eIdentification of manifold structures with local quadratic structures on the universal cover\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eKey tool\u003c\/td\u003e\n\u003ctd\u003eAlgebraic L-theory assembly map and fibre identification\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eAlgebraic L-theory and Topological Manifolds is a high-value reference for anyone researching surgery classification, the Novikov conjectures, or algebraic formulations of manifold invariants. Its focused, rigorous treatment makes it indispensable to specialists while its technical density means it is best purchased by readers with substantial background in topology and algebraic methods.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eDoes this book explain the algebraic L-theory assembly map?\u003c\/strong\u003e\u003cbr\u003eYes; the book centers on the assembly map, showing how it passes from local quadratic structures to global duality structures and identifying its fibre with the difference between manifold and Poincare duality homotopy types.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eIs this suitable for beginners in topology?\u003c\/strong\u003e\u003cbr\u003eNo; the text is research-level and assumes prior knowledge of chain complexes, Poincare duality spaces, and surgery theory rather than serving as an introductory course.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eDoes it address the Novikov conjectures?\u003c\/strong\u003e\u003cbr\u003eYes; it provides a purely algebraic formulation of the Novikov conjectures on homotopy invariance of higher signatures and explains how other formulations factor through this algebraic version.\u003c\/p\u003e","brand":"A. A. Ranicki","offers":[{"title":"Default Title","offer_id":48224383369435,"sku":"0521055210","price":72.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/51N26T34itL._SL1000.jpg?v=1770312243","url":"https:\/\/gearmusthave.com\/products\/algebraic-l-theory-and-topological-manifolds-definitive-survey","provider":"GearMustHave","version":"1.0","type":"link"}