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300   $a2 t. (VIII, 136 ;$c126 p.) ;$c30 cm.
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500   $aTit. orig.: Mastering math.
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101 0 $aeng
135   $aur|||||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 12$aA course on surgery theory /$fStanley Chang, Shmuel Weinberger$b[electronic resource]
210  1$aPrinceton :$cPrinceton University Press,$d2021.
215   $a1 online resource (472 p.) $c14 b/w illus
225 1 $aAnnals of mathematics studies ;$vnumber 211
225 1 $aPrinceton scholarship online
300   $aAlso issued in print: 2021.
311   $a0-691-16048-1 
320   $aIncludes bibliographical references and index.
327   $tFrontmatter -- $tContents -- $tList of Figures -- $tPreface -- $tIntroduction -- $t1 The characterization of homotopy types -- $t2 Some calculations of L-groups -- $t3 Classical surgery theory -- $t4 Topological surgery and surgery spaces -- $t5 Applications of the assembly map -- $t6 Beyond characteristic classes -- $t7 Flat and almost flat manifolds -- $t8 Other surgery theories -- $tAppendix A: Some background in algebraic topology -- $tAppendix B: Geometric preliminaries -- $tList of Symbols -- $tBibliography -- $tIndex
330 8 $aSurgery theory, a subfield of geometric topology, is the study of the classifications of manifolds. This book offers a modern look at this important mathematical discipline and some of its applications. In this book, Stanley Chang and Shmuel Weinberger explain some of the triumphs of surgery theory during the past three decades, from both an algebraic and geometric point of view. They also provide an extensive treatment of basic ideas, main theorems, active applications, and recent literature. The authors methodically cover all aspects of surgery theory, connecting it to other relevant areas of mathematics, including geometry, homotopy theory, analysis, and algebra. Later chapters are self-contained, so readers can study them directly based on topic interest.
410  0$aAnnals of mathematics studies ;$vnumber 211.
410  0$aPrinceton scholarship online.
606   $aSurgery (Topology)
610   $aBorel conjecture.
610   $aChapman-Ferry.
610   $aFarrell-Hsiang.
610   $aKirby-Siebenmann.
610   $aL-theory.
610   $aNovikov conjecture.
610   $aPL category.
610   $aPL topology.
610   $aalgebraic topology.
610   $aassembly map.
610   $aassembly perspective on surgery.
610   $abounded topology.
610   $aclassification of manifolds.
610   $acontrolled topology.
610   $adifferential topology.
610   $afibration.
610   $aflat manifolds.
610   $ahomology manifolds.
610   $ahomology surgery.
610   $ahomotopy invariant.
610   $ahomotopy theory.
610   $aindex theorem.
610   $ainduction theory.
610   $amanifold theory.
610   $aquadratic form theory.
610   $aquadratic form.
610   $arepresentation theory.
610   $asmooth category.
610   $asplitting theorems.
610   $astratified spaces.
610   $asurgery exact sequence.
610   $asurgery obstruction group.
610   $atangent bundle.
610   $atopological category.
610   $atopological surgery theory.
610   $atopology.
615  0$aSurgery (Topology)
676   $a605
686   $a415.7$2njb/10
700   $aChang$b Stanley$01217700
702   $aWeinberger$b Shmuel
801  0$bStDuBDS
801  1$bStDuBDS
906   $aBOOK
912   $a9910554281203321
996   $aA course on surgery theory$92815971
997   $aUNINA