The Reidemeister torsion of 3-manifolds /
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| Author / Creator: | Nicolaescu, Liviu I. |
|---|---|
| Imprint: | Berlin ; New York : Walter de Gruyter, c2003. |
| Description: | xiv, 249 p. : ill. ; 25 cm. |
| Language: | English |
| Series: | De Gruyter studies in mathematics 30 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4832746 |
Table of Contents:
- Introduction
- Notations and conventions
- 1. Algebraic preliminaries
- 1.1. The torsion of acyclic complexes of vector spaces
- 1.2. The determinant line of a chain complex
- 1.3. Basic properties of the torsion
- 1.4. Some generalizations
- 1.5. Abelian group algebras
- 1.6. Abelian harmonic analysis
- 2. The Reidemeister torsion
- 2.1. The Reidemeister torsion of a CW-complex
- 2.2. Fitting ideals
- 2.3. The Alexander function and the Reidemeister torsion
- 2.4. The Reidemeister torsion of 3-manifolds
- 2.5. Computing the torsion of 3-manifolds using surgery presentations
- 2.6. Plumbings
- 2.7. Applications
- 3. Turaev's refined torsion
- 3.1. Combinatorial Euler structures
- 3.2. Smooth Euler structures
- 3.3. U(2) and Spin[superscript c] (3)
- 3.4. Euler structures on 3-manifolds
- 3.5. The Reidemeister-Turaev torsion of Euler structures
- 3.6. Arithmetic properties of the Reidemeister-Turaev torsion of 3-manifolds
- 3.7. Axiomatic description of the Reidemeister-Turaev torsion of 3-manifolds
- 3.8. The torsion of rational homology 3-spheres. Part 1
- 3.9. Quadratic functions, spin[superscript c] structures and charges
- 3.10. The torsion of rational homology 3-spheres. Part 2
- 4. Alternative interpretations of the Reidemeister torsion
- 4.1. A gauge theoretic interpretation: Seiberg-Witten invariants
- 4.2. A Morse theoretic interpretation
- 4.3. A spectral interpretation: the Ray-Singer analytic torsion
- A. Algebra
- A.1. Formal Hodge theory
- A.2. Determinants and zeta functions
- A.3. Extensions of Abelian groups
- B. Topology
- B.1. How to compute the Alexander polynomial of a knot
- B.2. Dehn surgery and linking forms
- Bibliography
- Symbols
- Index