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ON OVERTWISTED CONTACT SURGERIES

Published online by Cambridge University Press:  03 May 2018

SINEM ONARAN*
Affiliation:
Department of Mathematics, Hacettepe University, 06800 Beytepe-Ankara, Turkey email [email protected]
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Abstract

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In this paper, we obtain a new result for overtwisted contact $(+1/n)$-surgery. We also give a counterexample to a conjecture by James Conway on overtwistedness of manifolds obtained by contact surgery.

Type
Research Article
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

Baker, K. L. and Etnyre, J., ‘Rational linking and contact geometry’, Prog. Math. 296 (2012), 1937.Google Scholar
Conway, J., ‘Transverse surgery on knots in contact 3-manifolds’, Preprint, arXiv:1409.7077.Google Scholar
Ding, F., Geiges, H. and Stipsicz, A. I., ‘Surgery diagrams for contact 3-manifolds’, Turk. J. Math. 28 (2004), 4174.Google Scholar
Durst, S. and Kegel, M., ‘Computing rotation and self-linking numbers in contact surgery diagrams’, Acta Math. Hungar. 150(2) (2016), 524540.CrossRefGoogle Scholar
Etnyre, J. B., ‘Introductory lectures on contact geometry’, in: Topology and Geometry of Manifolds, Athens (2001), Proceedings of Symposia in Pure Mathematics, 71 (American Mathematical Society, Providence, RI, 2003), 81107.Google Scholar
Etnyre, J. B., ‘Legendrian and transversal knots’, in: Handbook of Knot Theory (Elsevier, Amsterdam, 2005), 105185.CrossRefGoogle Scholar
Geiges, H., An Introduction to Contact Topology, Cambridge Studies in Advanced Mathematics, 109 (Cambridge University Press, Cambridge, 2008).Google Scholar
Geiges, H. and Onaran, S., ‘Legendrian rational unknots in lens spaces’, J. Symplectic Geom. 13 (2015), 1750.Google Scholar
Kegel, M., ‘The Legendrian knot complement problem’, Preprint, arXiv:1604.05196.Google Scholar
Lisca, P., Ozsváth, P., Stipsicz, A. I. and Szabó, Z., ‘Heegaard Floer invariants of Legendrian knots in contact three-manifolds’, J. Eur. Math. Soc. 11(6) (2009), 13071363.Google Scholar
Ozbagci, B., ‘A note on contact surgery diagrams’, Int. J. Math. 16(2) (2005), 8799.CrossRefGoogle Scholar
Wand, A., ‘Tightness is preserved by Legendrian surgery’, Ann. Math. 182(2) (2015), 723738.CrossRefGoogle Scholar