Mathematical Proceedings of the Cambridge Philosophical Society

Splitting homomorphisms and the Geometrization Conjecture

a1 Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, U.S.A.; e-mail:


This paper gives an algebraic conjecture which is shown to be equivalent to Thurston's Geometrization Conjecture for closed, orientable 3-manifolds. It generalizes the Stallings–Jaco theorem which established a similar result for the Poincaré Conjecture. The paper also gives two other algebraic conjectures; one is equivalent to the finite fundamental group case of the Geometrization Conjecture and the other is equivalent to the union of the Geometrization Conjecture and Thurston's Virtual Bundle Conjecture.

(Received June 28 1999)
(Revised December 23 1999)