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 T0 an incompressible torus boundary component of M such that the pair (M,T0) 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 F1, F2 in (M,T0) which intersect in graphs GFi=Fi∩Fj⊂Fi, {i,j}={1,2}, the maximal number of mutually parallel, consecutive, negative edges that may appear in GFi is nj+1, where nj=|∂Fj|. In this paper we show that the correct such bound is nj+2, give a partial classification of the pairs (M,T0) where the bound nj+2 is reached, and show that if Δ(∂F1,∂F2)⩾6 then the bound nj+2 cannot be reached; this latter fact allows for the short proof of the classification of the pairs (M,T0) with M a hyperbolic 3-manifold and Δ(∂F1,∂F2)⩾6 to work without change as outlined in Valdez-Sánchez (2007) [5].