Contact manifolds and Weinstein $h$-cobordisms

Abstract

International audienc

Legendrian submanifolds with Hamiltonian isotopic symplectizations

“…Indeed, we will construct in Section 4 two closed Legendrian submanifolds in R 15 which are smoothly isotopic and have Hamiltonian isotopic symplectizations but which are not Legendrian isotopic. Corresponding examples were described by the author in [4,Section 3] for the absolute case.…”

“…L.5; 1/, obtained by composing the inclusion of a factor with and then projection, would have degree 1. But then necessarily acts by multiplication by˙2 on 1 , in which case the Whitehead torsion of must be nonzero (see [4,Lemma 3.2]), contradicting the fact that is a diffeomorphism. Let .LI ƒ; ƒ/ be an h-cobordism given by the lemma above.…”