This book is intended as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes features of the multicomponent case not normally considered by knot theorists, such as longitudes, the homological complexity of many-variable Laurent polynomial rings, free coverings of homology boundary links, the fact that links are not usually 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.
Contents:
- 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
Readership: Graduate students and academics in geometry and topology.
