LEADER 04464nam 2200613 450 001 9910480014403321 005 20170816143330.0 010 $a1-4704-0650-0 035 $a(CKB)3360000000464427 035 $a(EBL)3113492 035 $a(SSID)ssj0000888811 035 $a(PQKBManifestationID)11539772 035 $a(PQKBTitleCode)TC0000888811 035 $a(PQKBWorkID)10875122 035 $a(PQKB)10432345 035 $a(MiAaPQ)EBC3113492 035 $a(PPN)195411269 035 $a(EXLCZ)993360000000464427 100 $a19810302h19811981 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCategorical framework for the study of singular spaces /$fWilliam Fulton and Robert MacPherson 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[1981] 210 4$dİ1981 215 $a1 online resource (173 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 243 300 $aDescription based upon print version of record. 311 $a0-8218-2243-8 320 $aBibliography: pages 162-165. 327 $a""Table of Contents""; ""Part I: Bivariant theories""; ""A?1 Survey""; ""1.1 Bivariant theories""; ""1.2 Grothendieck transformations""; ""1.3 Orientations and Gysin homomorphisms""; ""1.4 Formules of Riemann-Roch type""; ""1.5 An Example""; ""1.6 Guide to [BT]""; ""1.7 Acknowledgements""; ""A?2 Bivariant Theories""; ""2.1 The underlying category""; ""2.2 Axioms for a bivariant theory""; ""2.3 Associated contravariant and covariant functors""; ""2.4 External products""; ""2.5 Gysin homomorphisms""; ""2.6 Orientations""; ""2.7 Grothendieck transformations""; ""A?3 Topological Theories"" 327 $a""3.1 Construction of a bivariant theory from a cohomology theory""""3.2 Grothendieck transformations of topological theories""; ""3.3 Supports""; ""3.4 Specialization""; ""A?4 Orientations in Topology""; ""4.1 Normally non-singular maps""; ""4.2 Cohomology operations""; ""4.3 Differentiable Riemann-Roch""; ""A?5 Transfer and Fixed Point Index""; ""A?6 Whitney Classes""; ""6.1 The bivariant theory FF""; ""6.2 The Grothendieck transformation I??""; ""6.3 Consequences of Theorem 6A""; ""6.4 Proof of uniqueness of I??""; ""6.5 Construction of I??""; ""6.6 Applications"" 327 $a""A?7 Grothendieck Duality and Derived Functors""""7.1 Grothendieck duality""; ""7.2 Duality and Riemann-Roch""; ""7.3 Homology from derived functors""; ""7.4 Etale theory""; ""A?8 Operational Theories""; ""A?9 Rational Equivalence and Intersection Formulas""; ""9.1 Operational rational equivalence theory""; ""9.2 Intersection formulas""; ""A?10 Other Bivariant Theories; Open Problems""; ""10.1 Fixed point theorems for coherent sheaves""; ""10.2 Finite groups""; ""10.3 Orientations in algebraic geometry""; ""10.4 Chern classes""; ""10.5 Equivariant Whitney classes""; ""10.6 Verdier duality"" 327 $a""10.7 Non-submersive maps in topology""""10.8 Independent squares for algebraic K-theory""; ""10.9 Uniqueness questions""; ""10.10 Analytic Riemann-Roch""; ""10.11 Rational equivalence""; ""10.12 Higher K-theory""; ""10.13 Geometric interpretation of bivariant homology elements""; ""Part II: Products in Riemann-Roch""; ""A?0 Introduction""; ""0.1 Some history""; ""0.2 Summary of results""; ""0.3 Plan of the proof""; ""A?1 Statement of the theorem""; ""1.1 Bivariant algebraic K-theory""; ""1.2 Morphisms of finite Tor dimension""; ""1.3 Local complete intersection morphisms"" 327 $a""1.4 The Riemann-Roch theorem""""1.5 The Chern character""; ""1.6 Riemann-Roch with supports""; ""A?2 Complexes""; ""2.1 Topological complexes""; ""2.2 Some homological algebra""; ""2.3 An application""; ""2.4 The main lemma""; ""A?3 Proof of the theorem""; ""References"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 243. 606 $aHomology theory 606 $aCategories (Mathematics) 608 $aElectronic books. 615 0$aHomology theory. 615 0$aCategories (Mathematics) 676 $a510 s 676 $a514/.24 700 $aFulton$b William$f1939-$041611 702 $aMacPherson$b Robert$f1944- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480014403321 996 $aCategorical framework for the study of singular spaces$92162218 997 $aUNINA