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arXiv · 1412.0828

On Stein fillings of contact torus bundles

Marco Golla·Paolo Lisca
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Abstract

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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Marco Golla, Paolo Lisca. 2015-10-28. On Stein fillings of contact torus bundles. https://doi.org/10.1112/blms%2Fbdv082

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