H-3(DIFF(-2)Z) CONTAINS AN UNCOUNTABLE Q-VECTOR SPACE()(S)

We describe a subgroup Q of H-3(Diff(+)(S-2);Z) With the following pro perties: (i) the characteristic classes of group actions defined by Bo tt [1] induce a surjection from Q to R(2), and (ii) Q is divisible. Th e definition of Q was suggested by a paper of Rasmussen [14] in which he constructs a family of elements of H-5(B Gamma(2); Z) which surject s onto R(2) under the characteristic classes of foliations. To prove t he divisibility we use results of Dupont, Parry, Sah, Suslin, and Wago ner on the homology of Lie groups made discrete. The suspension of Q w hich associates to every element of Q its associated S-2-bundle gives a subgroup of H-5(B Gamma(2); Z) isomorphic to R(2).