Mathematical Research Letters

Volume 17 (2010)

Number 6

Milnor fillable contact structures are universally tight

Pages: 1055 – 1063

DOI: https://dx.doi.org/10.4310/MRL.2010.v17.n6.a5

Authors

Yanki Lekili (Mathematical Sciences Research Institute, Berkeley, CA)

Burak Ozbagci (Mathematical Sciences Research Institute, Berkeley, CA)

Abstract

We show that the canonical contact structure on the link of a normal complex singularity is universally tight. As a corollary we show the existence of closed, oriented, atoroidal $3$-manifolds with infinite fundamental groups which carry universally tight contact structures that are not deformations of taut (or Reebless) foliations. This answers two questions of Etnyre in \cite{etn}.

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Published 1 January 2010