C. S. Pintea (Babes-Bolyai University), The size of the critical sets of various functions

In this lecture I am going to provide information on the size of critical sets and the sets of critical values, in terms of cardinality or dimension, for various types of differentiable maps, including Morse functions. Pairs of manifolds which only admit functions with infinitely many critical points will be pointed out along with pairs of manifolds which admit functions with finitely many critical points. For the first ones we sometimes evaluate the critical sets in terms of dimension and for the latter ones the minimum number of critical points is usually provided.