Exotic characteristic classes for holomorphic foliations

Abstract

In this paper we will construct examples which show that a large number of characteristic classes for complex (holomorphic) foliations vary continuously and independently. This generalizes the results of Baum-Bott [2], and is a generalization of our results in the real case (Rasmussen [10]). In w 1 we will start by defining the classes that we are interested in. In w 2 we will give the Baum-Bott construction, which shows that all the exotic classes in H2q+I(B~C; C) vary continuously and independently. In w we will modify and simplify their computations. Finally in w using the new technique we will compute new classes and it will be seen how this new method gives more than Baum-Bott [2], to be precise we detect all the products of the classes in [2] that is elements of H 4q § 2 (Bl.qC; C), they are all non-zero and vary continuously and independently in a way we will make precise later. Similarly we detect related classes in H4q+l(B~C; C), they are also non-zero and vary continuously and independently and the variations give surjective maps