COMPARING HEEGAARD AND JSJ STRUCTURES OF ORIENTABLE 3-MANIFOLDS

MARTIN SCHARLEMANN JENNIFER SCHULTENS

Abstract. The Heegaard genus g of an irreducible closed orientable 3-manifold puts a limit on the number and complexity of the pieces that arise in the Jaco-Shalen-Johannson decomposition of the manifold by its canonical tori. For example, if p of the complementary components are not Seifert fibered, then p ≤ g − 1. This generalizes work of Kobayashi [?]. The Heegaard genus g also puts explicit bounds on the complexity of the Seifert pieces. For example, if the union of the Seifert pieces has base space P and f exceptional fibers, then

f − χ(P) ≤ 3g − 3 − p.