Stein fillings and \(\operatorname{SU}(2)\) representations
Stein structures on a single 4-manifold with distinct Chern classes modulo torsion determine some contact structures on a 3-manifold. The properties of the contact invariants of such contact structures are considered. It is proved that if a 3-manifold bounds a so-called Stein domain of special type, then the fundamental group of the contact structure of the manifold admits a nontrivial homomorphism to the group \(\text{SU}(2)\).
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