Singularities of ray systems. (English) Zbl 0566.58004

Proc. Int. Congr. Math., Warszawa 1983, Vol. 1, 27-49 (1984).
[For the entire collection see Zbl 0553.00001.]
This is a summary of the author’s plenary address to the international congress of mathematicians in Warsaw 1983. It reviews – proofless, but with quite a few examples on hand – recent work (mainly from the last decade) of A. B. Givental’, O. V. Lyashko, O. A. Platatsova, I. G. Shcherbak and others, not to forget the author himself, on the relations between singularities of ray systems and reflection groups, also known as Lagrangian and Legendrian singularity theory in symplectic and in contact geometry. The article is profitably read together with the author’s paper in [Russ. Math. Surv. 38, No. 2, 87–176 (1983); translation from Usp. Mat. Nauk 38, No. 2(230), 77–147 (1983; Zbl 0522.58007)].
Reviewer: H.Crauel


58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
58K35 Catastrophe theory
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems