The geometry and physics of knots. (English) Zbl 0729.57002

Atiyah, Michael

Accademia Nazionale dei Lincei. Lezioni Lincee. Cambridge etc.: Cambridge University Press. x, 78 p. £20.00/hbk; $ 39.50/hbk; £6.95/pbk; $ 14.95/pbk (1990).

In this lucid and insightful monograph the author provides an elegant introduction for graduate students and researchers to the pioneering work of Vaughan Jones and Edward Witten relating polynomial invariants of knots to a topological quantum field theory in \(2+1\) dimensions. This book presents a mathematical introduction to Witten’s ideas and is essential reading for all geometers, gauge theorists, and those mathematicians that want to be exposed to a large amount of intriguing and exciting ideas that form the kernel of a new and rapidly developing research area.

Reviewer: R.Stern (Salt Lake City)

MSC:

57M25	Knots and links in the \(3\)-sphere (MSC2010)
35Q40	PDEs in connection with quantum mechanics
46N50	Applications of functional analysis in quantum physics
57-02	Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes

Keywords:

path integral; moduli; skein relations; polynomial invariants; knots; topological quantum field theory