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This paper completely determines the obstructions to fibering a class co s f over S 3 and S* (the two solutions are precisely the same). As consequences we obtain results for some other 3 and 4-manifolds. We also get a partial description of the fibering ideal of S 2 x S 2 and offer a conjecture as to what the complete answer should be. In addition, since almost all the fibrations we construct over the spheres actually fiber over CP(3), and since all obstruc-doi:10.1215/ijm/1256046799 fatcat:ncyprz4wx5eghjzebgzoajx75q