Contact Structures on elliptic 3-manifolds

الأصل · EN

We show that an oriented elliptic 3-manifold admits a universally tight positive contact structure iff the corresponding group of deck transformations on S³ preserves a standard contact structure pointwise. We also relate univerally tight contact structures on 3-manifolds covered by S³ to the exceptional isomorphism SO(4)=(SU(2)× SU(2))/± 1. The main tool used is equivariant framings of 3-manifolds.