Torsion in Kauffman bracket skein module of a 4‐strand Montesinos knot exterior

Abstract For an oriented 3‐manifold , let denote its Kauffman bracket skein module over . We show that admits torsion when is the exterior of the Montesinos knot with each . This provides a negative answer to Problem 1.92 (G)–(i) in the Kirby's list, which asks whether is free when is irreducible and has no incompressible nonboundary parallel torus.