Topology of the Milnor fibrations of polar weighted homogeneous polynomials

摘要

Let P be a 2-variable polar weighted homogeneous polynomial and let Ft be a deformation of P which is also a polar weighted homogeneous polynomial. If | Ft | is a Morse function on the orbit space of the S1-action, then the handle decomposition obtained by this Morse function induces a round handle decomposition of the Milnor fibration of Ft. In the present paper, we describe a round handle decomposition of the Milnor fibration of Ft concretely and give the number of round handles by the number of positive and negative components of the links of singularities appearing before and after the deformation. We also give a formula of characteristic polynomials of these singularities by using the decomposition of the monodromy of the Milnor fibration induced by a round handle decomposition.