Topology of the Milnor fibrations of polar weighted homogeneous polynomials

2016/09/20 by Kazumasa Inaba, Inaba, Kazumasa
Mathematics · #32S30 #32S40 #32S55 #57M25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1609.06132

openalex publication_date 2016/09/20 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In the present paper, we study deformations of polar weighted homogeneous polynomials which are also polar weighted homogeneous polynomials. We describe a round handle decomposition of the Milnor fibration of a deformation of a polar weighted homogeneous polynomial 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.

Related

• Fold singularities of the maps associated with Milnor fibration for mixed polynomials
• On deformations of isolated singularities of polar weighted homogeneous mixed polynomials
• The singularities of the maps associated with Milnor fibrations
• Bicomplex polar weighted homogeneous polynomials
• Deformation of Milnor Algebras