The Reidemeister Torsion of 3-Manifolds

Liviu I. Nicolaescu

Published by De Gruyter 2003

The Reidemeister Torsion of 3-Manifolds

Liviu I. Nicolaescu

Volume 30 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110198102

Overview
Contents

About this book

This is a state-of-the-art introduction to the work of Franz Reidemeister, Meng Taubes, Turaev, and the author on the concept of torsion and its generalizations. Torsion is the oldest topological (but not with respect to homotopy) invariant that in its almost eight decades of existence has been at the center of many important and surprising discoveries. During the past decade, in the work of Vladimir Turaev, new points of view have emerged, which turned out to be the "right ones" as far as gauge theory is concerned.

The book features mostly the new aspects of this venerable concept. The theoretical foundations of this subject are presented in a style accessible to those, who wish to learn and understand the main ideas of the theory. Particular emphasis is upon the many and rather diverse concrete examples and techniques which capture the subleties of the theory better than any abstract general result. Many of these examples and techniques never appeared in print before, and their choice is often justified by ongoing current research on the topology of surface singularities.

The text is addressed to mathematicians with geometric interests who want to become comfortable users of this versatile invariant.

Author / Editor information

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

Reviews

"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

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	i
Contents Requires Authentication Unlicensed Licensed Download PDF	xiii
Chapter 1. Algebraic preliminaries Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 2. The Reidemeister torsion Requires Authentication Unlicensed Licensed Download PDF	44
Chapter 3. Turaev’s refined torsion Requires Authentication Unlicensed Licensed Download PDF	106
Chapter 4. Alternative interpretations of the Reidemeister torsion Requires Authentication Unlicensed Licensed Download PDF	174
Appendix A. Algebra Requires Authentication Unlicensed Licensed Download PDF	197
Appendix B. Topology Requires Authentication Unlicensed Licensed Download PDF	210
Backmatter Requires Authentication Unlicensed Licensed Download PDF	239

(Deutsch)

Language: English
Publisher: De Gruyter
Pages
- Front matter: 14
- Main content: 249
Keywords: Dreidimensionale Mannigfaltigkeit; Knoten (Math.)

eBook

Published: August 22, 2008
ISBN: 9783110198102

Hardcover

Published: January 24, 2003
ISBN: 9783110173833