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A generalization of Thom’s transversality theorem

Lukáš Vokřínek (2008)

Archivum Mathematicum

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 of A where the...

A regularity lemma for functions of several variables.

Jean L. Journé (1988)

Revista Matemática Iberoamericana

We shall prove the following Theorem. Let Fs and Fu be two continuous transverse foliations with uniformly smooth leaves, of some manifold. If f is uniformly smooth along the leaves of Fs and Fu, then f is smooth.

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