Exceptional Dehn surgeries on some infinite series of hyperbolic knots and links (Q6623423)

A Dehn surgery on a knot in a hyperbolic 3-manifold is called \textit{exceptional} if it yields a non-hyperbolic 3-manifold. Such surgeries are only finitely many for a given knot by Thurston's hyperbolic Dehn surgery theorem, and thus, there are numerous studies on this topic. In the paper under review, the authors consider and study Dehn surgeries on some components of a 4-component link, introduced and studied by \textit{K. Motegi} and \textit{H.-J. Song} [Algebr. Geom. Topol. 5, 369--378 (2005; Zbl 1083.57012)], and \textit{K. Ichihara} et al. [Bull. Nara Univ. Educ., Nat. Sci. 57, No. 2, 21--25 (2008; Zbl 1479.57013)], by using finite balanced group presentations of the fundamental groups of the obtained manifolds. As an application, for every integer \(n > 5\), they obtain infinitely many hyperbolic knots in the 3-sphere on which \((n-2)\)- and \((n + 1)\)-surgeries are toroidal, and \((n-1)\)- and \(n\)-surgeries are Seifert fibered.