This book serves as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes the features of the multicomponent case not normally considered by knot-theorists, such as longitudes, the homological complexity of many-variable Laurent polynomial rings, the fact that links are not usually boundary links, free coverings of homology boundary links, the lower central series as a source of invariants, nilpotent completion and algebraic closure of the link group, and disc links. Invariants of the types considered here play an essential role in many applications of knot theory to other areas of topology.This second edition introduces two new chapters - twisted polynomial invariants and singularities of plane curves. Each replaces brief sketches in the first edition. Chapter 2 has been reorganized, and new material has been added to four other chapters.
Abelian Covers: Links; Homology and Duality in Covers; Determinantal Invariants; The Maximal Abelian Cover; Sublinks and Other Abelian Covers; Twisted Polynomial Invariants; Applications: Special Cases and Symmetries: Knot Modules; Links with Two Components; Symmetries; Singularities of Plane Curves; Free Covers, Nilpotent Quotients and Completion: Free Covers; Nilpotent Quotients; Algebraic Closure; Disc Links.