Corrigendum to “Toroidal and Klein bottle boundary slopes” [Topology Appl. 154 (3) (2007) 584–603]

Let M be a compact, connected, orientable, irreducible 3-manifold and T 0 an incompressible torus boundary component of M such that the pair ( M , T 0 ) is not cabled. In the paper “Toroidal and Klein bottle boundary slopes” (2007) [5] by the author it was established that for any K -incompressible tori F 1 , F 2 in ( M , T 0 ) which intersect in graphs G F i = F i ∩ F j ⊂ F i , { i , j } = { 1 , 2 } , the maximal number of mutually parallel, consecutive, negative edges that may appear in G F i is n j + 1 , where n j = | ∂ F j | . In this paper we show that the correct such bound is n j + 2 , give a partial classification of the pairs ( M , T 0 ) where the bound n j + 2 is reached, and show that if Δ ( ∂ F 1 , ∂ F 2 ) ⩾ 6 then the bound n j + 2 cannot be reached; this latter fact allows for the short proof of the classification of the pairs ( M , T 0 ) with M a hyperbolic 3-manifold and Δ ( ∂ F 1 , ∂ F 2 ) ⩾ 6 to work without change as outlined in Valdez-Sánchez (2007) [5].