In Dae Jong

Alexander polynomials of alternating knots of genus two

In this paper we will characterize rational tangle surgeries on 2-bridge knot b(2m, 2n) yielding a (2, 2k)-torus link. As an application, we will characterize particular lens space surgeries on knots in lens spaces with good symmetry.

Cyclic and finite surgeries on Montesinos knots

We give a complete classification of the Dehn surgeries on Montesinos knots which yield manifolds with cyclic or finite fundamental groups.

ALEXANDER POLYNOMIALS OF ALTERNATING KNOTS OF GENUS TWO II

We give a family of linear inequalities which strictly estimate relation among the coefficients of the Alexander polynomials of alternating knots of genus two. We also give such families for positive knots of genus two, and for homogeneous knots of genus two. As an application, we determine the alternating knots of genus two such that the leading coefficients of them are less than or equal to three.