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Higher Complex Torsion and the Framing Principle.

By: Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2005Copyright date: ©2005Edition: 1st edDescription: 1 online resource (114 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470404369
Subject(s): Genre/Form: Additional physical formats: Print version:: Higher Complex Torsion and the Framing PrincipleDDC classification:
  • 510 s;514/.72
LOC classification:
  • QA613.4 -- .I38 2005eb
Online resources:
Contents:
Intro -- Contents -- Introduction -- 0.1. Higher Franz-Reidemeister torsion -- 0.2. Construction of τ[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 FR-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 FR-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.
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Intro -- Contents -- Introduction -- 0.1. Higher Franz-Reidemeister torsion -- 0.2. Construction of τ[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 FR-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 FR-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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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