03677nam 2200613 450 991047986500332120170822144505.01-4704-0436-2(CKB)3360000000465019(EBL)3114252(SSID)ssj0000973209(PQKBManifestationID)11539950(PQKBTitleCode)TC0000973209(PQKBWorkID)10958883(PQKB)10349562(MiAaPQ)EBC3114252(PPN)195417232(EXLCZ)99336000000046501920050429h20052005 uy| 0engur|n|---|||||txtccrHigher complex torsion and the framing principle /Kiyoshi IgusaProvidence, Rhode Island :American Mathematical Society,[2005]©20051 online resource (114 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 835"Volume 177, number 835 (third of 4 numbers)."0-8218-3773-7 Includes bibliographical references.""Contents""; ""Introduction""; ""0.1. Higher Franz-Reidemeister torsion""; ""0.2. Construction of Ï?[sub(k)]""; ""0.3. Framing Principle""; ""0.4. Complex torsion""; ""Chapter 1. Complex torsion""; ""1.1. Definition for closed AC fibers""; ""1.2. Generalized Miller-Morita-Mumford classes""; ""1.3. Complex Framing Principle""; ""1.4. Nonempty boundary case""; ""Chapter 2. Definition of higher FRâ€?torsion""; ""2.1. Generalized Morse functions""; ""2.2. Families of chain complexes""; ""2.3. Monomial functors""; ""2.4. Filtered chain complexes""; ""2.5. Subfunctors""""2.6. The Whitehead category""""2.7. Definition in acyclic case""; ""2.8. Families of matrices as flat superconnections""; ""2.9. Independence of birth-death points""; ""2.10. Positive suspension lemma""; ""2.11. Definition in upper triangular case""; ""Chapter 3. Properties of higher FRâ€?torsion""; ""3.1. Basic properties""; ""3.2. Suspension Theorem""; ""3.3. Additivity, Splitting Lemma""; ""3.4. Applications of the Splitting Lemma""; ""3.5. Local equivalence lemma""; ""3.6. Product formula""; ""3.7. Transfer for coverings""; ""3.8. More transfer formulas""""Chapter 4. The Framing Principle""""4.1. Statement for Morse bundles""; ""4.2. General statement""; ""4.3. Push-down/transfer""; ""4.4. The Framing Principle""; ""Chapter 5. Proof of the Framing Principle""; ""5.1. Transfer theorem""; ""5.2. Stratified deformation lemma""; ""5.3. Proof of transfer theorem""; ""5.4. Proof of Framing Principle""; ""Chapter 6. Applications of the Framing Principle""; ""6.1. Torelli group""; ""6.2. Even dimensional fibers""; ""6.3. Unoriented fibers""; ""6.4. Vertical normal disk bundle""; ""Chapter 7. The Stability Theorem""; ""7.1. Definitions""""7.2. Stability for C(M)""""7.3. Involution""; ""7.4. Disks and spheres""; ""7.5. Relation to higher torsion""; ""Bibliography""Memoirs of the American Mathematical Society ;no. 835.Reidemeister torsionDifferentiable mappingsDiffeomorphismsElectronic books.Reidemeister torsion.Differentiable mappings.Diffeomorphisms.510 s514/.72Igusa Kiyoshi1949-894342MiAaPQMiAaPQMiAaPQBOOK9910479865003321Higher complex torsion and the framing principle1997857UNINA