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Singularities cancellation on wave fronts

โœ Scribed by Emmanuel Ferrand

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
130 KB
Volume
95
Category
Article
ISSN
0166-8641

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โœฆ Synopsis

We show that any Legendre knot in the contact manifold of cooriented contact elements of a surface M is, up to stabilization, Legendre-isotopic to a Legendre knot whose projection on M (wave front) is an immersion, provided that it is Legendre-homotopic to such a knot. As a consequence, we obtain that each ambient isotopy class of knots contains Legendre representatives with immersed wave fronts. We also show that similar results do not hold in the context of the manifold of noncooriented contact elements.

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RbumC. There exists a Legendrian embedding ! c ST'R" such that: (i) any &' in the same Legendrian ~.FOIOI)): class has a non-immersed front and (ii) there exists t" in the same Legendrian homorop?, class whose front is immersed. 0 Academic des ScienceslElsevier. Paris Singular-it& non kliminables su