On the bi-Lipschitz contact equivalence of plane complex function-germs

Lev Birbrair, Alexandre Fernandes, Vincent Grandjean

Journal of Singularities
volume 13 (2015), 1-10

Received 14 August 2013. Received in revised form 20 August 2014.

DOI: 10.5427/jsing.2015.13a

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Abstract:

In this note, we consider the problem of bi-Lipschitz contact equivalence of complex analytic function-germs of two variables. Basically, it is inquiring about the infinitesimal sizes of such function-germs up to bi-Lipschitz changes of coordinates. We show that this problem is equivalent to right topological classification of such function-germs.


Mathematical Subject Classification:

14B05, 32S05, 58K50


Author(s) information:

Lev Birbrair Alexandre Fernandes Vincent Grandjean
Departamento de Matemática Departamento de Matemática Departamento de Matemática
Universidade Federal do Ceará Universidade Federal do Ceará Universidade Federal do Ceará
Campus do Picici, Bloco 914 Campus do Picici, Bloco 914 Campus do Picici, Bloco 914
Cep. 60455-760. Fortaleza-Ce, Brasil Cep. 60455-760. Fortaleza-Ce, Brasil Cep. 60455-760. Fortaleza-Ce, Brasil
email: birb@ufc.br email: alexandre.fernandes@ufc.br email: vjhgrgr@gmail.com