Topological equivalence of complex polynomials

Arnaud Bodin; Mihai Tibar

doi:10.1016/j.aim.2005.03.003

paper

Topological equivalence of complex polynomials

arXiv:math/0309316 · doi:10.1016/j.aim.2005.03.003

Abstract

The following numerical control over the topological equivalence is proved: two complex polynomials in $n \neq = 3$ variables and with isolated singularities are topologically equivalent if one deforms into the other by a continuous family of polynomial functions $f_{s} : C^{n} \to C$ with isolated singularities such that the degree, the number of vanishing cycles and the number of atypical values are constant in the family.

14 pages, revised text for final version