H3(Diff+(S2);Z) Contains an uncountable Q-vector space

We describe a subgroup Q of H3(Diff+(S2);Z) with the following properties: 1. e characteristic classes of group actions defined by Bott [1] induce a surjection from Q to R2, and is divisible. efinition of Q was suggested by a paper of Rasmussen [14] in which he constructs a family of elements of H5(BΓ2; Z) which surjects onto R2 under the characteristic classes of foliations. To prove the divisibility we use results of Dupont, Parry, Sah, Suslin, and Wagoner on the homology of Lie groups made discrete. The suspension of Q which associates to every element of Q its associated S2-bundle gives a subgroup of H5(BΓ2; Z) isomorphic to R2.