Stein fillings and \(\operatorname{SU}(2)\) representations. (English) Zbl 1407.57019
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 \(\text{SU}(2)\).
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 \(\text{SU}(2)\).
Reviewer: Mihail Banaru (Smolensk)
MSC:
| 57R17 | Symplectic and contact topology in high or arbitrary dimension |
| 57M27 | Invariants of knots and \(3\)-manifolds (MSC2010) |
| 57R58 | Floer homology |
Keywords:
contact structure; contact invariant; Stein domain; homology; \(\text{SU}(2)\) representationReferences:
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