Higher complex torsion and the framing principle / / Kiyoshi Igusa

• Record Nr.: UNINA9910788749803321
• Autore: Igusa Kiyoshi <1949->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2005]; ©2005
• ISBN: 1-4704-0436-2
• Descrizione fisica: 1 online resource (114 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 835
• Disciplina: 510 s; 514/.72
• Soggetti: Reidemeister torsion; Differentiable mappings; Diffeomorphisms
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 177, number 835 (third of 4 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""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""