The Geometry and Physics of Knots

Michael Atiyah (Author)

9780521395540, Cambridge University Press

Paperback, published 23 August 1990

108 pages
21.5 x 13.7 x 0.7 cm, 0.123 kg

"The exposition is taut and the writing simple, elegant, and to the point. It is in fact a tour de force of single-minded and jargon-free exposition....we are dealing here more with poetry and inspirational writing than with the prose of everyday mathematics, and in this spirit, it is a pleasure to recommend this little volume to one and all." Raoul Bott, Bulletin of the American Mathematical Society

These notes arise from lectures presented in Florence under the auspices of the Accadamia dei Lincee and deal with an area that lies at the crossroads of mathematics and physics. The material presented here rests primarily on the pioneering work of Vaughan Jones and Edward Witten relating polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions. Professor Atiyah here presents an introduction to Witten's ideas from the mathematical point of view. The book will be essential reading for all geometers and gauge theorists as an exposition of new and interesting ideas in a rapidly developing area.

Preface
1. History and background
2. Topological quantum field theories
3. Non-abelian moduli spaces
4. Symplectic quotients
5. The infinite-dimensional case
6. Projective flatness
7. The Feynman integral formulation
8. Final comments
Bibliography
Index.

Subject Areas: Geometry [PBM]