Contact Structures on elliptic 3-manifolds

Siddhartha Gadgil

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Contact Structures on elliptic 3-manifolds

Siddhartha Gadgil

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Abstract

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

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Siddhartha Gadgil. 2002-08-29. Contact Structures on elliptic 3-manifolds. https://arxiv.org/abs/math/0112271

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