Contact structures on elliptic $3$-manifolds
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- by Siddhartha Gadgil PDF
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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.References
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Additional Information
- Siddhartha Gadgil
- Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794
- Address at time of publication: Stat-Math Unit, Indian Statistical Institute, 8th Mile, Mysore Road, R. V. College post, Bangalore 560059, India
- Email: gadgil@math.sunysb.edu
- Received by editor(s): March 1, 2002
- Received by editor(s) in revised form: August 20, 2002
- Published electronically: July 22, 2004
- Communicated by: Ronald A. Fintushel
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 132 (2004), 3705-3714
- MSC (2000): Primary 53D10, 57M50
- DOI: https://doi.org/10.1090/S0002-9939-04-07572-0
- MathSciNet review: 2084095