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Contact structures on elliptic -manifolds
Authors:Siddhartha Gadgil
Institution:Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794
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.

Keywords:
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