Displaying similar documents to “Normal forms for certain singularities of vectorfields”

Holonomy groups of complete flat manifolds

Michał Sadowski (2007)

Banach Center Publications

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We present short direct proofs of two known properties of complete flat manifolds. They say that the diffeomorphism classes of m-dimensional complete flat manifolds form a finite set S C F ( m ) and that each element of S C F ( m ) is represented by a manifold with finite holonomy group.

A generalization of Thom’s transversality theorem

Lukáš Vokřínek (2008)

Archivum Mathematicum

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We prove a generalization of Thom’s transversality theorem. It gives conditions under which the jet map f * | Y : Y J r ( D , M ) J r ( D , N ) is generically (for f : M N ) transverse to a submanifold Z J r ( D , N ) . We apply this to study transversality properties of a restriction of a fixed map g : M P to the preimage ( j s f ) - 1 ( A ) of a submanifold A J s ( M , N ) in terms of transversality properties of the original map f . Our main result is that for a reasonable class of submanifolds A and a generic map f the restriction g | ( j s f ) - 1 ( A ) is also generic. We also present an example...

Simple singularities of multigerms of curves.

Pavel A. Kolgushkin, Ruslan R. Sadykov (2001)

Revista Matemática Complutense

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We classify stably simple reducible curve singularities in complex spaces of any dimension. This extends the same classification of irreducible curve singuarities obtained by V. I. Arnold. The proof is essentially based on the method of complete transversals by J. Bruce et al.

A construction of a connection on G Y Y from a connection on Y M by means of classical linear connections on M and Y

Włodzimierz M. Mikulski (2005)

Commentationes Mathematicae Universitatis Carolinae

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Let G be a bundle functor of order ( r , s , q ) , s r q , on the category m , n of ( m , n ) -dimensional fibered manifolds and local fibered diffeomorphisms. Given a general connection Γ on an m , n -object Y M we construct a general connection 𝒢 ( Γ , λ , Λ ) on G Y Y be means of an auxiliary q -th order linear connection λ on M and an s -th order linear connection Λ on Y . Then we construct a general connection 𝒢 ( Γ , 1 , 2 ) on G Y Y by means of auxiliary classical linear connections 1 on M and 2 on Y . In the case G = J 1 we determine all general connections...

The contact system on the ( m , ) -jet spaces

J. Muñoz, F. J. Muriel, Josemar Rodríguez (2001)

Archivum Mathematicum

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This paper is a continuation of [MMR:98], where we give a construction of the canonical Pfaff system Ω ( M m ) on the space of ( m , ) -velocities of a smooth manifold M . Here we show that the characteristic system of Ω ( M m ) agrees with the Lie algebra of Aut ( m ) , the structure group of the principal fibre bundle M ˇ m J m ( M ) , hence it is projectable to an irreducible contact system on the space of ( m , ) -jets ( = -th order contact elements of dimension m ) of M . Furthermore, we translate to the language of Weil bundles the structure...

On second order Thom-Boardman singularities

László M. Fehér, Balázs Kőműves (2006)

Fundamenta Mathematicae

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We derive closed formulas for the Thom polynomials of two families of second order Thom-Boardman singularities Σ i , j . The formulas are given as linear combinations of Schur polynomials, and all coefficients are nonnegative.