Splitting homomorphisms and the Geometrization Conjecture

Details Splitting homomorphisms and the Geometrization Conjecture Splitting homomorphisms and the Geometrization Conjecture

1999-06-18

arxiv.org/abs/math/9906124v2

Mathematics

Geometric Topology

11 pages, Some typos are corrected

Scientific paper

10.1017/S0305004100004631

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 Poincare 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.

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