Contents -- Preface -- Part 1. Abelian Covers -- Chapter 1. Links -- 1.1. Basic notions -- 1.2. The link group -- 1.3. Homology boundary links -- 1.4. Z/2Z-boundary links -- 1.5. Isotopy concordance and /-equivalence -- 1.6. Link homotopy and surgery -- 1.7. Ribbon links -- 1.8. Link-symmetric groups -- 1.9. Link composition -- Chapter 2. Homology and Duality in Covers -- 2.1. Homology and cohomology with local coefficients -- 2.2. Covers of link exteriors -- 2.3. Poincare duality and the Blanchfield pairings -- 2.4. The total linking number cover -- 2.5. The maximal abelian cover -- 2.6. Concordance -- 2.7. Additivity -- 2.8. The Seifert approach for boundary 1-links -- 2.9. Signatures -- Chapter 3. Determinantal Invariants -- 3.1. Elementary ideals -- 3.2. The Elementary Divisor Theorem -- 3.3. Extensions -- 3.4. Reidemeister-Franz torsion -- 3.5. Steinitz-Fox-Smythe invariants -- 3.6. 1- and 2-dimensional rings -- 3.7. Bilinear pairings -- Chapter 4. The Maximal Abelian Cover -- 4.1. Metabelian groups and the Crowell sequence -- 4.2. Free metabelian groups -- 4.3. Link module sequences -- 4.4. Localization of link module sequences -- 4.5. Chen groups -- 4.6. Applications to links -- 4.7. Chen groups nullity and longitudes -- 4.8. I-equivalence -- 4.9. The sign-determined Alexander polynomial -- 4.10. Higher dimensional links -- Chapter 5. Sublinks and Other Abelian Covers -- 5.1. The Torres conditions -- 5.2. Torsion again -- 5.3. Partial derivatives -- 5.4. The total linking number cover -- 5.5. Murasugi nullity -- 5.6. Fibred links -- 5.7. Finite abelian covers -- 5.8. Cyclic branched covers -- 5.9. Families of coverings -- 5.10. Twisted Alexander invariants -- Part 2. Applications: Special Cases and Symmetries -- Chapter 6. Knot Modules -- 6.1. Knot modules -- 6.2. A Dedekind criterion -- 6.3. Cyclic modules.

6.4. Recovering the module from the polynomial -- 6.5. Homogeneity and realizing TT-primary sequences -- 6.6. The Blanchfield pairing -- 6.7. Branched covers -- Chapter 7. Links with Two Components -- 7.1. Bailey's Theorem -- 7.2. Consequences of Bailey's Theorem -- 7.3. The Blanchfield pairing -- 7.4. Links with Alexander polynomial 0 -- 7.5. 2-Component Z/2Z-boundary links -- 7.6. Topological concordance and F-isotopy -- 7.7. Some examples -- Chapter 8. Symmetries -- 8.1. Basic notions -- 8.2. Symmetries of knot types -- 8.3. Group actions on links -- 8.4. Semifree periods -- 8.5. Links with infinitely many semifree periods -- 8.6. Knots with free periods -- 8.7. Strong symmetries -- 8.8. Equivariant concordance -- Part 3. Free Covers Nilpotent Quotients and Completion -- Chapter 9. Free Covers -- 9.1. Free group rings -- 9.2. Z[F(u)]-Modules -- 9.3. The Sato property -- 9.4. The Farber derivations -- 9.5. The maximal free cover and duality -- 9.6. The classical case -- 9.7. The case n = 2 -- 9.8. An unlinking theorem -- 9.9. Patterns and calibrations -- 9.10. Concordance -- Chapter 10. Nilpotent Quotients -- 10.1. Massey products -- 10.2. Products the Dwyer filtration and gropes -- 10.3. Mod-p analogues -- 10.4. The graded Lie algebra of a group -- 10.5. DGAs and minimal models -- 10.6. Milnor invariants -- 10.7. Link homotopy and the Milnor group -- 10.8. Variants of the Milnor invariants -- 10.9. Solvable quotients and covering spaces -- Chapter11. Algebraic Closure -- 11.1. Homological localization -- 11.2. The nilpotent completion of a group -- 11.3. The algebraic closure of a group -- 11.4. Complements on F(u) -- 11.5. ther notions of closure -- 11.6. Orr invariants and cSHB-links -- Chapter12. Disc Links -- 12.1. Disc links and string links -- 12.2. Longitudes.

12.3. Concordance and the Artin representation -- 12.4. Homotopy -- 12.5. Milnor invariants again -- 12.6. The Gassner representation -- 12.7. High dimensions -- Bibliography -- Index.