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Knots. 3rd fully revised and extented edition. (English) Zbl 1283.57002

De Gruyter Studies in Mathematics 5. Berlin: Walter de Gruyter (ISBN 978-3-11-027074-7/hbk; 978-3-11-027078-5/ebook). xiii, 417 p. (2014).
This is the third edition of the worldwide famous book on knots. For reviews of the first and second editions, see [Zbl 0568.57001] and [Zbl 1009.57003]. One author is added, and some sections are greatly rewritten. For example, in Chapter 3, a solution of the Property \(P\) conjecture by P. Kronheimer and T. Mrowka [Geom. Topol. 8, 295–310 (2004; Zbl 1072.57005)] is commented. In Chapter 5, a condition on fiberedness of satellite knots by M. Hirasawa et al. [Hiroshima Math. J. 38, No. 3, 411–423 (2008; Zbl 1180.57011)] is described.
Moreover, a new chapter, which includes a proof of Schubert’s theorem about the additivity of bridge number, is added. The original argument is long and written in German, but this chapter adopts a shorter argument byJ. Schultens [Math. Proc. Camb. Philos. Soc. 135, No. 3, 539–544 (2003; Zbl 1054.57011)].
The bibliography was reduced to include only references cited in the book. Also, the knot table in the appendix was reduced.

MSC:

57-02 Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes
57-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57M50 General geometric structures on low-dimensional manifolds
20F34 Fundamental groups and their automorphisms (group-theoretic aspects)
20F36 Braid groups; Artin groups
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