Topological triviality of families of map germs from R^2 to R^2

J.A. Moya-Pérez and J. J. Nuño-Ballesteros

Journal of Singularities
volume 6 (2012), 112-123
Proceedings of the Workshop on Singularities in Geometry and Applications, Będlewo, 5 – 21 May 2011

Received: 30 December 2011. Received in revised form: 4 April 2012.

DOI: 10.5427/jsing.2012.6i

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We show that a 1-parameter unfolding F: (R^2 x R, 0) → (R^2 x R, 0) of a finitely determined map germ f is topologically trivial if it is excellent in the sense of Gaffney and the family of the discriminant curves Δ(f_t) is topologically trivial. We also give a formula to compute the number of cusps of 1-parameter unfoldings.


stable map, link, topological triviality

Mathematical Subject Classification:

Primary 58K15; Secondary 58K40, 58K60

Author(s) information:

L. Birbrair J. J. Nuño-Ballesteros
Departament de Geometria i Topologia Departament de Geometria i Topologia
Universitat de València Universitat de València
Campus de Burjassot Campus de Burjassot
46100 Burjassot SPAIN 46100 Burjassot SPAIN
email: email: