4 papers
Proof of the metric Arnold's corank problem
Aexandre Fernandes, Zbigniew Jelonek, José Edson Sampaio
In this article, we approach the Arnold corank problem, posed by Arnold in 1975, which asks whether the corank of holomorphic functions is an ambient topological invariant. Here, w…
On the Milnor fibres of initial forms of topologically equivalent holomorphic functions
José Edson Sampaio
Budur, Fernandes de Bobadilla, Le and Nguyen (2022) conjectured that if two germs of holomorphic functions are topologically equivalent, then the Milnor fibres of their initial for…
On the topological invariance of the algebraic multiplicity of holomorphic foliations
Leonardo M. Câmara, Fernando Reis, José Edson Sampaio
In this paper, we address one of the most basic and fundamental problems in the theory of foliations and ODEs, the topological invariance of the algebraic multiplicity of a holomor…
The multiplicity mod 2 is not a bi-lipschitz invariant
A. Fernandes, Z. Jelonek, J. E. Sampaio
We show that subanalytic bi-Lipschitz homeomorphisms in general does not preserve the multiplicities of real analytic sets.