By G.P. Joubert, R.P. Moussu, R.H. Roussarie

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Define ~f*(V) with p r o j e c t i o n called the bundle Let Suppose V : f*V--~X ~f,~) W by f properties X V of c o n s t r u c t i n g be a map in (x,v) = x. vector bundle over G v e c t o r bundles Y. of Then over or the induced bundle. 31, we m e n t i o n are LC(G) such that subspace ~f,~)(x,v) G of vector bundles. invariant is a induced by and G is a ~X. real or complex, the set of points is a module over D(V) methods f : X---~Y vector bundle, As an a p p l i c a t i o n sum. ~D(V) ; ~D(Vf G module.

Vector bundle over G v e c t o r bundles Y. of Then over or the induced bundle. 31, we m e n t i o n are LC(G) such that subspace ~f,~)(x,v) G of vector bundles. invariant is a induced by and G is a ~X. real or complex, the set of points is a module over D(V) methods f : X---~Y vector bundle, As an a p p l i c a t i o n sum. ~D(V) ; ~D(Vf G module. which in turn is a module the functorial This h*(X) h*fD(V),S(V)) from existing f*V h*(X) is an two important induced bundle. Let f*V which is x e h*(X).

1: H e Dc(G ) real F A e VOW G which I II vii i i, II wll I II~II = I, [lw][ ! I}. handle is G Z and H with <__ i} isotropy homeomorphic to group G×FD~(V) F for some module. 2 Let same dimension. attaching X We say that a handle H with be elements Z of is obtained isotropy group Dc(G) from F X of the by and index if: (i) F is module W (ii) (iii) V is a real such that F module and there H = G×FD'(V~W ). Z = X u H. H~X = H ~ ~X = G×FSv(V~W ). 3 [14] Let X without boundry) in submanifold with G disk bundle Dc(G ).