The Reidemeister Torsion of 3-Manifolds

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.

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

"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