Abstract
Let P be a 2-variable polar weighted homogeneous polynomial and let \(F_t\) be a deformation of P which is also a polar weighted homogeneous polynomial. If \(|F_{t}|\) is a Morse function on the orbit space of the \(S^1\)-action, then the handle decomposition obtained by this Morse function induces a round handle decomposition of the Milnor fibration of \(F_t\). In the present paper, we describe a round handle decomposition of the Milnor fibration of \(F_t\) 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.
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Inaba, K. Topology of the Milnor fibrations of polar weighted homogeneous polynomials. manuscripta math. 157, 411–424 (2018). https://doi.org/10.1007/s00229-018-0998-z
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DOI: https://doi.org/10.1007/s00229-018-0998-z