The Reidemeister Torsion of 3-Manifolds

Liviu I. Nicolaescu (Autor)

Buch | Hardcover

XIV, 249 Seiten

2003
De Gruyter (Verlag)
978-3-11-017383-3 (ISBN)

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The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics.While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics.While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

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

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

"It is very well written, with many examples and also many exercises."EMS Newsletter "This very readable book provides an introduction to the theory of torsion."St. Haller in: Monatshefte für Mathematik 3/2004

"It is very well written, with many examples and also many exercises."
EMS Newsletter

"This very readable book provides an introduction to the theory of torsion."
St. Haller in: Monatshefte für Mathematik 3/2004

"This useful and well-written book gives an introduction to current developments in the theory and applications of Reidemeister torsion. [...] The particular strength of Nicolaescu's book is perhaps in the examples and its nature as a `user's guide' to torsion. These aspects will make it equally valuable to both established researchers and graduate students trying to gain experience in the field." Mathematical Reviews

Erscheint lt. Verlag	24.1.2003
Reihe/Serie	De Gruyter Studies in Mathematics ; 30
Verlagsort	Berlin/Boston
Sprache	englisch
Maße	170 x 240 mm
Gewicht	575 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Allgemeines, Lexika • analytic torsion • chain complex • Dimension 3 • Dreidimensionale Mannigfaltigkeit • EALT20/4 • Geometry • Geometry and Topology • Hardcover, Softcover / Mathematik/Allgemeines, Lexika • HC/Mathematik/Allgemeines, Lexika • HC/Mathematik/Geometrie • Hodge Theory • Homology • Homotopy • Knoten (Math.) • manifold • Mann • Mannigfaltigkeit • Mathematics • prosodic • Reidemeister torsion • Reidemeister-Torsion • System • Three-manifolds (Topology) • V.D.HULST • WORD
ISBN-10	3-11-017383-2 / 3110173832
ISBN-13	978-3-11-017383-3 / 9783110173833
Zustand	Neuware