Sufficiency of jets with line singularities | Zendy

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Sufficiency of jets with line singularities

Author(s) -

Brodersen Hans

Publication year - 2009

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/bdp016

Subject(s) - mathematics , gravitational singularity , invariant (physics) , jet (fluid) , combinatorics , homeomorphism (graph theory) , manifold (fluid mechanics) , line (geometry) , pure mathematics , mathematical analysis , geometry , mathematical physics , physics , mechanical engineering , engineering , thermodynamics

Let z : (ℝ n + 1 , 0) → (ℝ, 0) be an r ‐jet with a singular set containing a 1‐dimensional manifold L . Letℛ 0 Lbe the set of homeomorphism germs h : (ℝ n + 1 , 0) → (ℝ n + 1 , 0) leaving L invariant. Letε [ r ] Lbe the set of C r germs, f : (ℝ n + 1 , 0) → (ℝ, 0), with singular sets containing L . We say that z is sufficient inε [ r ] Lif any two f and g inε [ r ] Lwithj r f ( 0 ) = j r g ( 0 ) = z areℛ 0 L ‐equivalent. In this paper we give necessary and sufficient conditions in terms of Łojasiewicz inequalities for such a jet z to be sufficient inε [ r ] L .

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