Singularity links with exotic Stein fillings

Journal of Singularities
volume 8 (2014), 39-49

Received: 24 December 2013. Received in revised form: 4 February 2014.

DOI: 10.5427/jsing.2014.8d

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Abstract:

In [4], it was shown that there exist infinitely many contact Seifert fibered 3-manifolds each of which admits infinitely many exotic (homeomorphic but pairwise non-diffeomorphic) simply-connected Stein fillings. Here we extend this result to a larger set of contact Seifert fibered 3-manifolds with many singular fibers and observe that these 3-manifolds are singularity links. In addition, we prove that the contact structures induced by the Stein fillings are the canonical contact structures on these singularity links. As a consequence, we verify a prediction of András Némethi by providing examples of isolated complex surface singularities whose links with their canonical contact structures admitting infinitely many exotic simply-connected Stein fillings. Moreover, for infinitely many of these contact singularity links and for each positive integer n, we also construct an infinite family of exotic Stein fillings with fixed fundamental group isomorphic to the direct sum of Z and Z_n.

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