o 36 where ~C ~ isa submodule defined by can be thought of as an element Hl(M,HOmo(~(g*),~*)). group of a smooth non-singular singular foliation this approach ~0" Again this sequence ~(~(P,~0) ) Whereas foliation, in the sheaf cohomology this group is zero in the case it can be non-trivial even in the smooth case, which is one reason why is of interest.
Xn_ q spanning The partially horizontal vectorfields Q. ,Yq X I, .... Xn_ q with respect to form together with a basis of fundamental vectorfields framing of Tp. ,Gq belonging to the corresponding dual local ~i(Xj) = 8ij, particular Bi(~j) = 8ij 81, .... 44) locally a be the 1-forms framing of are a local framing of ~ c g*. ,Yq T~, Bi(Xj) = O. so that In v'Q*. 45) ~ :~n(~i,~j)~i A ~j i