Nicolaescu The Reidemeister Torsion of 3-Manifolds

1. Auflage 2008
ISBN: 978-3-11-019810-2
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 263 Seiten, Gewicht: 10 g

Reihe: ISSN

Autoren/Hrsg.

Nicolaescu, Liviu I.

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

Algebraic Preliminaries · The torsion of acyclic complexes of vector spaces · The determinant line of a chain complex · Basic properties of the torsion · Some generalizations · Abelian group algebras · Abelian harmonic analysis · The Reidemeister Torsion · The Reidemeister torsion of a CW-complex · Fitting ideals · The Alexander function and the Reidemeister torsion · The Reidemeister torsion of 3-manifolds · Computing the torsion of 3-manifolds using surgery presentations · Plumbings · Applications · Turaev's Refined Torsion · Combinatorial Euler structures · Smooth Euler structures · U(2) and Spinc(3) · Euler structures on 3-manifolds · The Reidemeister-Turaev torsion of Euler structures · Arithmetic properties of the Reidemeister-Turaev torsion of 3-manifolds · Axiomatic description of the Reidemeister-Turaev torsion of 3-manifolds · The torsion of rational homology 3-spheres. Part 1 · Quadratic functions, Spinc structures and charges · The torsion of rational homology 3-spheres. Part 2 · Alternative Interpretations of the Reidemeister Torsion · A gauge theoretic interpretation: Seiberg-Witten invariants · A Morse theoretic interpretation · A spectral interpretation: the Ray-Singer analytic torsion · Algebra · Formal Hodge theory · Determinants and zeta functions · Extensions of Abelian groups · Topology · How to compute the Alexander polynomial of a knot · Dehn surgery and linking forms
Bibliography

Über Autor(innen)

Liviu Nicolaescu is Professor at the University of Notre Dame, Indiana, USA.