# Contact Structures on elliptic 3-manifolds

Authors
Type
Preprint
Publication Date
Aug 29, 2002
Submission Date
Dec 24, 2001
Identifiers
arXiv ID: math/0112271
Source
arXiv
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.