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Knots. 2nd revised and extended ed. (English) Zbl 1009.57003
de Gruyter Studies in Mathematics. 5. Berlin: Walter de Gruyter. xii, 559 p. (2003).
In this second edition (for a review of the first one (1985) see Zbl 0568.57001), according to the corresponding preface, some mistakes have been corrected, some chapters have been improved (chapter ten with a proof of Markov’s theorem on braids, chapter fifteen with a statement of the Gordon-Luecke Theorem on knot complements) and the last chapter has been added. It deals with the HOMFLY polynomial constructed with help of the Hecke algebras which are introduced. It generalizes the Alexander-Conway polynomial and the Jones polynomial. The bibliography has been enhanced including mention to books on knots which have been published since the first edition.

MSC:
57-02 Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
20F34 Fundamental groups and their automorphisms (group-theoretic aspects)
20F36 Braid groups; Artin groups
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