PreprintGeometric decompositions of 4dimensional bundle spacesJonathan A. HillmanAbstractWe consider geometric decompositions of aspherical 4manifolds which fibre over 2orbifolds. We show first that no such manifold admits infinitely many fibrations over hyperbolic base orbifolds. If E is Seifert fibred over a hyperbolic base B and either B has at most one cone point or order 2 or the monodromy is in SL(2,Z) then E has a decomposition induced from a decomposition of B. Keywords: cusp, decomposition, geometry, orbifold, Seifert, 4manifold.AMS Subject Classification: Primary 57N13.
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