Introduction to Combinatorial Torsions [Paperback]

Vladimir Turaev (Author)

Book Description

Series: Lectures in Mathematics. ETH Zürich | Publication Date: March 1, 2001

This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds. The first two chapters cover algebraic foundations of the theory of torsions and various topological constructions of torsions due to K. Reidemeister, J.H.C. Whitehead, J. Milnor and the author. We also discuss connections between the torsions and the Alexander polynomials of links and 3-manifolds. The third (and last) chapter of the book deals with so-called refined torsions and the related additional structures on manifolds, specifically homological orientations and Euler structures. As an application, we give a construction of the multivariable Conway polynomial of links in homology 3-spheres. At the end of the book, we briefly describe the recent results of G. Meng, C.H. Taubes and the author on the connections between the refined torsions and the Seiberg-Witten invariant of 3-manifolds. The exposition is aimed at students, professional mathematicians and physicists interested in combinatorial aspects of topology and/or in low dimensional topology. The necessary background for the reader includes the elementary basics of topology and homological algebra.

Editorial Reviews

Review

"[The book] contains much of the needed background material in topology and algebra…Concering the considerable material it covers, [the book] is very well-written and readable." --Zentralblatt Math

Product Details

• Paperback: 131 pages
• Publisher: Birkhäuser Basel; 1 edition (March 1, 2001)
• Language: English
• ISBN-10: 3764364033
• ISBN-13: 978-3764364038
• Product Dimensions: 9.4 x 6.7 x 0.4 inches
• Shipping Weight: 10.2 ounces
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #3,211,156 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

2 of 2 people found the following review helpful:

5.0 out of 5 stars Excellent book, August 16, 2001

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hqvn "hqvn" (NY, United States) - See all my reviews

This review is from: Introduction to Combinatorial Torsions (Paperback)

This short book is a good place to start learning about the theory of Reidemeister torsions. Masterfully written by one of the leading experts on the subject, it follows the standard of exposition set by Milnor in his famous survey on this subject 40 years ago. The book is very easy to read, the necessary background is covered economically, but in details. You can find here many results that received the first treatment in book form and some classical results with illuminating explainations. The last chapter briefly indicates recent developments in connection with Seiberg-Witten invariants of 3-manifolds.

The book is mainly an introduction and concerns mostly with combinatorial manifolds and knot theory. As the author stated, many other aspects of the theory (e.g. the analytical theory) are left out.