Algebraic invariants of links (Q2894725)

This book is an introduction to links and more particularly to invariants of abelian coverings of link exteriors, with a presentation of several topics related to free coverings, nilpotent quotients and concordance. The invariants that are studied may be used in the concordance classification of classical knots, in the Casson-Freedman analysis of topological surgery problems and in other areas of topology.NEWLINENEWLINEThe first edition of this book was reviewed in this database by Alberto Cavicchioli [Series on Knots and Everything. 32. Singapore: World Scientific (2002; Zbl 1007.57001)], and that review contains a summary of the content of each chapter.NEWLINENEWLINEThe new edition contains a new chapter (Chapter 6) on \textit{Twisted polynomial Invariants}. It concerns notably the twisted Alexander polynomials associated to a linear representation of a knot group and their homological formulation as a Reidemeister-Franz torsion presented in terms of local coefficients. Twisted Alexander polynomials were first defined by X.-S. Lin using the free differential calculus. The material in this chapter was the subject of the last section of Chapter 5 in the first edition.NEWLINENEWLINEThe new edition contains also a new chapter (Chapter 10) on \textit{Singularities of Plane Curves}. Furthermore, Chapter 2 has been rewritten and and new material has been added to Chapter 7 (\textit{Knot Modules}) and Chapter 12 (\textit{Nilpotent Quotients}).