Topological equivalence of complex polynomials

Arnaud Bodin, Mihai Tibar

Published 2003-09-19, updated 2005-03-14Version 2

The following numerical control over the topological equivalence is proved: two complex polynomials in $n\not= 3$ variables and with isolated singularities are topologically equivalent if one deforms into the other by a continuous family of polynomial functions $f_s \colon \mathbb{C}^n \to \mathbb{C}$ with isolated singularities such that the degree, the number of vanishing cycles and the number of atypical values are constant in the family.