Introduction to Combinatorial Torsions
Edition: 1 edition
Publisher: Birkhäuser Basel
Published: March 1, 2001
Language: eng
Format: Paperback
Number of pages: 123
ISBN-13: 9783764364038
Subjects: Differential & Riemannian geometry; Mathematics for scientists & engineers; Riemannian Manifolds; Algebraic Topology; Mathematics; Science/Mathematics; Geometry - Algebraic; Combinatorics; Geometry - General; Mathematics / General; Geometry - Differential; Topology - General
First sentence: Let F be a field and let D be a finite-dimensional vector space over F.
Description: 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.