Surfaces incompressibles dans les variétés obtenues par chirurgie longitudinale le long d'un noeud de $S^3$

Dehn filling with non-degenerate boundary slope rows

“…We remark that Corollary 3 is no longer true if n 3. For example, let M be the exterior of the Borromean ring in S 3 . Then M has no closed essential surfaces but Dehn filling M along any one of the three components of ∂M with the meridian slope produces a reducible manifold (here is an argument that M does not contain any closed essential surfaces).…”

“…Example 7. Let M be the exterior of the Whitehead link in S 3 . Then M has infinitely many non-degenerated boundary slope rows of length 2.…”

“…There are several versions of Handle Addition Lemma. The first one was due to Przytycki [11] and subsequently generalized and used in various forms in [1,3,[7][8][9]13,14]. The version stated above is from [1].…”

“…We remark that one of useful consequences of Theorem 1 is that under the assumptions of Theorem 1, if M(r) is an irreducible 3-manifold which is not Haken, then M contains an essential closed surface. For instance, if M is the exterior of a knot in S 3 whose meridian slope is a boundary slope, then M contains an essential closed surface.…”