04464nam 2200613 450 991048001440332120170816143330.01-4704-0650-0(CKB)3360000000464427(EBL)3113492(SSID)ssj0000888811(PQKBManifestationID)11539772(PQKBTitleCode)TC0000888811(PQKBWorkID)10875122(PQKB)10432345(MiAaPQ)EBC3113492(PPN)195411269(EXLCZ)99336000000046442719810302h19811981 uy| 0engur|n|---|||||txtccrCategorical framework for the study of singular spaces /William Fulton and Robert MacPhersonProvidence, Rhode Island :American Mathematical Society,[1981]©19811 online resource (173 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 243Description based upon print version of record.0-8218-2243-8 Bibliography: pages 162-165.""Table of Contents""; ""Part I: Bivariant theories""; ""Â1 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""; ""Â2 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""; ""Â3 Topological Theories""""3.1 Construction of a bivariant theory from a cohomology theory""""3.2 Grothendieck transformations of topological theories""; ""3.3 Supports""; ""3.4 Specialization""; ""Â4 Orientations in Topology""; ""4.1 Normally non-singular maps""; ""4.2 Cohomology operations""; ""4.3 Differentiable Riemann-Roch""; ""Â5 Transfer and Fixed Point Index""; ""Â6 Whitney Classes""; ""6.1 The bivariant theory FF""; ""6.2 The Grothendieck transformation Ï?""; ""6.3 Consequences of Theorem 6A""; ""6.4 Proof of uniqueness of Ï?""; ""6.5 Construction of Ï?""; ""6.6 Applications""""Â7 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""; ""Â8 Operational Theories""; ""Â9 Rational Equivalence and Intersection Formulas""; ""9.1 Operational rational equivalence theory""; ""9.2 Intersection formulas""; ""Â10 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""""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""; ""Â0 Introduction""; ""0.1 Some history""; ""0.2 Summary of results""; ""0.3 Plan of the proof""; ""Â1 Statement of the theorem""; ""1.1 Bivariant algebraic K-theory""; ""1.2 Morphisms of finite Tor dimension""; ""1.3 Local complete intersection morphisms""""1.4 The Riemann-Roch theorem""""1.5 The Chern character""; ""1.6 Riemann-Roch with supports""; ""Â2 Complexes""; ""2.1 Topological complexes""; ""2.2 Some homological algebra""; ""2.3 An application""; ""2.4 The main lemma""; ""Â3 Proof of the theorem""; ""References""Memoirs of the American Mathematical Society ;no. 243.Homology theoryCategories (Mathematics)Electronic books.Homology theory.Categories (Mathematics)510 s514/.24Fulton William1939-41611MacPherson Robert1944-MiAaPQMiAaPQMiAaPQBOOK9910480014403321Categorical framework for the study of singular spaces2162218UNINA