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Register a new userUniqueness of contact Hamiltonians of topological strictly contact isotopies
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We prove that for regular contact forms there exists a bijective correspondence between the $C^0$ limits of sequences of smooth strictly contact isotopies and the limits with respect to the contact distance of their corresponding Hamiltonians.
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We prove that any small enough neighborhood of a closed contact submanifold is always tight under a mild assumption on its normal bundle. The non-existence of $C^0$--small positive loops of contactomorphisms in general overtwisted manifolds is shown as a corollary.
We consider a large family F of torus bundles over the circle, and we use recent work of Li--Mak to construct, on each Y in F, a Stein fillable contact structure C. We prove that (i) each Stein filling of (Y,C) has vanishing first Chern class and first Betti number, (ii) if Y in F is elliptic then all Stein fillings of (Y,C) are pairwise diffeomorphic and (iii) if Y in F is parabolic or hyperbolic then all Stein fillings of (Y,C) share the same Betti numbers and fall into finitely many diffeomorphism classes. Moreover, for infinitely many hyperbolic torus bundles Y in F we exhibit non-homotopy equivalent Stein fillings of (Y,C).
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