Hi, everyone: I am trying to find a result for the number of bundles (up to bundle iso.) over a fixed base and fixed fiber. For example, for B=S<sup>1</sup> , and fiber I=[0,1] I think that there are two; the cylinder and the Mobius strip. I think that the reason there are two (classes of) bundles is that there are only two isotopy classes in Hom(I,I) , where Hom is a homeomorphism; the class of the identity, and the class of the map f(t)=1-t, so that one copy of I . Also: how can we count the number of bundles over S<sup>1</sup> x S<sup>1</sup>.? The obvious bundles are the ones defined as product bundles of the bundles above, i.e., cylinderxcylinder, etc. Is there a way of knowing if the product bundles are the only bundles over S<sup>1</sup> x S<sup>1</sup>.? I guess if the above ideas is correct, we should consider the isotopy classes of Hom(IxI,IxI ). Thanks.