## A classification of automorphisms of compact 3-manifolds |

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1-dimensional lamination 1-handles 3-manifold adjusting automorphism assume automorphism g automorphisms of handlebodies back-tracks body Q boundary spheres bounds a disc classification of automorphisms closed reducing surface complete system compression body connected sum consider constructed contained corresponding decompose Dehn twist denote disc in H disjoint union distinct spots embedded essential discs essential spheres graph growth rate Heegaard splitting height function holed balls homeomorphism homotopy equivalence incidence matrix induced automorphism interior boundary invariant laminations isotopy class isotopy rel Kt,Vt Kti+1 Kti+l Lemma mapping class group mixed body neighborhood non-rigid obtain orbifold periodic pseudo-Anosov Recall rectangles Rti regular values restriction Section Seifert fibered space sphere boundary components sphere components spinal pair Pt,Vt spotted ball spotted component spotted manifold spotted product subspinal pair sum of S2 surface F Theorem 1.5 train track transverse measure unholed half-disc unique unlinking move yields