Geometric decompositions of 4-dimensional bundle spaces

Jonathan A. Hillman

Abstract

We consider geometric decompositions of aspherical 4-manifolds which fibre over 2-orbifolds. 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, 4-manifold.

AMS Subject Classification: Primary 57N13.