Kohno, Toshitake (ed.) New developments in the theory of knots. (English) Zbl 0727.57001 Advanced Series in Mathematical Physics, 11. Singapore etc.: World Scientific. ix, 906 p. $ 86.00/hbk; $ 48.00/pbk (1990). [The articles of this volume will not be indexed individually.] This collection of reprints written by outstanding scientists describes the progress in mathematics and physics following the discovery of a new topological polynomial invariant for knots and links by V. Jones in 1985. In mathematics this discovery led first of all to the construction of a variety of one- and two-variable generalizations of the Jones polynomial that appeared to be a powerful tool for the solution of many long- standing classical problems in knot theory. In physics these new polynomials were shown to be related to solutions of the Yang-Baxter equations describing 2-dimensional soluble statistical mechanical models and monodromies of \(1+1\)-dimensional conformal field theory. The book gives a comprehensive and full account on recent developments and deep interrelations of new results in modern mathematical physics and will be useful for all scholars aiming to enter quickly to this new and promising field of science. Reviewer: E.D.Belokolos (Kiev) Cited in 1 ReviewCited in 3 Documents MSC: 57-06 Proceedings, conferences, collections, etc. pertaining to manifolds and cell complexes 00B60 Collections of reprinted articles 57M25 Knots and links in the \(3\)-sphere (MSC2010) Keywords:Knots; Reprints; polynomial invariant; knots; links; Jones polynomial; Yang-Baxter equations; statistical mechanical models; conformal field theory PDFBibTeX XMLCite \textit{T. Kohno} (ed.), New developments in the theory of knots. Singapore etc.: World Scientific (1990; Zbl 0727.57001)