A₀-sufficiency of jets from R² to R²

Hans Brodersen and Olav Skutlaberg

Journal of Singularities
volume 2 (2010), 19-50
Proceedings of Singularities in Aarhus, August 2009

Received: 23 November 2009.

DOI: 10.5427/jsing.2010.2b

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Abstract:

An r-jet z in J^r(2,2) is A₀-sufficient in E_[r](2,2) if every C^r realization of z is topologically right-left equivalent to z. We give sufficient conditions for A₀-sufficiency in E_[r](2,2). For a certain class of jets, we prove that our sufficient conditions are also necessary. Finally, we use the techniques developed in the course of the proofs of these results to give sufficient conditions for a 1-parameter family of C^r plane-to-plane map-germs to be topologically trivial.

Keywords:

Sufficiency of jets, finite determinacy, jets from the plane to the plane

Mathematical Subject Classification:

14B05, 58A20 (primary), 58A20 (secondary)

Author(s) information:

Hans Brodersen	Olav Skutlaberg
Department of Mathematics, University of Oslo	Department of Mathematics, University of Oslo
P.B. 1053, 0316 Oslo	P.B. 1053, 0316 Oslo
Norway	Norway
email: broderse@math.uio.no	email: oskutlab@math.uio.no