Contact structures on elliptic 3-manifolds

Gadgil, Siddhartha

doi:10.1090/S0002-9939-04-07572-0

Contact structures on elliptic $3$-manifolds
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by Siddhartha Gadgil

Proc. Amer. Math. Soc. 132 (2004), 3705-3714

DOI: https://doi.org/10.1090/S0002-9939-04-07572-0

Published electronically: July 22, 2004

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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.

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