Critical point theory in mathematics and in mathematical physics. (English) Zbl 0889.58021

Bott, Raoul

Turk. J. Math. 21, No. 1, 9-40 (1997).

This paper contains the exposition of a conference held by the author on some results on new knot invariants introduced by Axelrod, Singer and Kontsevich in the study of 3-manifold invariants. The author shows how these invariants arise out of physics-inspired considerations. The exposition is given in the most comprehenable ferm for mathematicians.
In the opinion of the author, the different role of Morse theory in classical mechanics and quantum mechanics is the basic starting point of the matter.

Reviewer: A.Masiello (Bari)

MSC:

58E05	Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
57M25	Knots and links in the \(3\)-sphere (MSC2010)

Keywords:

critical point theory; classical mechanics; quantum mechanics; knot invariants; 3-manifold invariants; Morse theory