Contact structures on elliptic $3$-manifolds

Abstract

We show that an oriented elliptic $3$-manifold admits a universally tight positive contact structure if and only if the corresponding group of deck transformations on $S^3$ (after possibly conjugating by an isometry) preserves the standard contact structure. We also relate universally tight contact structures on $3$-manifolds covered by $S^3$ to the isomorphism $SO(4)=(SU(2)\times SU(2))/{\pm 1}$. The main tool used is equivariant framings of $3$-manifolds.

Locations

• Proceedings of the American Mathematical Society - View - PDF