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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Contact structures on elliptic $3$-manifolds


Author: Siddhartha Gadgil
Journal: Proc. Amer. Math. Soc. 132 (2004), 3705-3714
MSC (2000): Primary 53D10, 57M50
Published electronically: July 22, 2004
MathSciNet review: 2084095
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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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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

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07572-0
PII: S 0002-9939(04)07572-0
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
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.