AN INVARIANT DERIVED FROM THE ALEXANDER POLYNOMIAL FOR HANDLEBODY-KNOTS

Abstract

A handlebody-knot is a handlebody embedded in the 3-sphere. We introduce an invariant for handlebody-knots derived from their Alexander polynomials. The value of the invariant is a vertex-weighted graph. As an application, we describe a sufficient condition for a handlebody-knot to be irreducible and a necessary condition for a link to be a constituent link of a handlebody-knot.