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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An r-jet z in Jr(2,2) is A0-sufficient in E[r](2,2) if every Cr 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 Cr plane-to-plane map-germs to be topologically trivial.


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