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Bulletin of the London Mathematical Society Advance Access originally published online on March 22, 2009
Bulletin of the London Mathematical Society 2009 41(3):445-457; doi:10.1112/blms/bdp016
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© 2009 London Mathematical Society

Sufficiency of jets with line singularities

Hans Brodersen

Department of Mathematics
University of Oslo
PB 1053, Blindern
NO-0316 Oslo
Norway
www.math.uio.no

Received 24 January 2008. Revision received 30 October 2008.

Let z: (R n + 1, 0) -> (R, 0) be an r-jet with a singular set containing a 1-dimensional manifold L. Let Formula be the set of homeomorphism germs h : (R n + 1, 0) -> (R n + 1, 0) leaving L invariant. Let Formula be the set of Cr germs, f : (R n + 1, 0) -> (R , 0), with singular sets containing L. We say that z is sufficient in Formula if any two f and g in Formula with Formula are Formula -equivalent. In this paper we give necessary and sufficient conditions in terms of Lojasiewicz inequalities for such a jet z to be sufficient in Formula .

2000 Mathematics Subject Classification 58K40 (primary), 14B05, 58A35 (secondary).


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