Series on Knots and Everything - Vol. 32
ALGEBRAIC INVARIANTS OF LINKS
by Jonathan Hillman (The University of Sydney, Australia)
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
- Applications: Special Cases and Symmetries:
- Knot Modules
- Links with Two Components
- Symmetries
- Free Covers, Nilpotent Quotients and Completion:
- Free Covers
- Nilpotent Quotients
- Algebraic Closure
- Disc Links
Readership: Graduate students and academics in geometry and topology.
"The author, who is one of the major experts on the topic, must be surely congratulated for this attractive book, written in a careful, very precise and quite readable style. It serves as an excellent self-contained and up-to-date monograph on the algebraic invariants of links ... I strongly recommend this beautiful book to anyone interested in the algebraic theory of links and its applications."
"Jonathan Hillman has successfully filled an unfortunate gap in the literature of low-dimensional topology ... With this up-to-date book we have a reference covering a range of topics that until now were available only in their original sources ... Hillman has done an excellent job of referencing his book, both within the text and in the bibliography, with several hundred references included."
| 320pp |
Pub. date: Oct 2002 |
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