Dehn surgery on arborescent knots
A knot \(K\) is called an arborescent knot if it can be obtained by summing and gluing several rational tangles together; see [\textit{D. Gabai}, Mem. Am. Math. Soc. 339, 1-98 (1986; Zbl 0585.57003)] for more detailed definitions. Recall that a 3-manifold is called a Haken manifold if it is irreducible and contains an incompressible surface. Following \textit{A. Hatcher} [Ann. Inst. Fourier 42, 313-325 (1992; Zbl 0759.57006)] we say that a 3-manifold \(M\) is laminar if it contains an essential lamination. The purpose of this paper is to study Dehn surgeries on arborescent knots, and to see which of these surgered manifolds are laminar, Haken, or hyperbolic.
scientific article; zbMATH DE number 895021