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Splitting homomorphisms and the Geometrization Conjecture

Published online by Cambridge University Press:  16 October 2000

ROBERT MYERS
Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, U.S.A.; e-mail: myersr@math.okstate.edu

Abstract

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.

Type
Research Article
Copyright
2000 Cambridge Philosophical Society

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