Legendre Düğümlerinin Sınıflandırılması
Loading...
Date
Authors
Pekavcılar, Berna
Journal Title
Journal ISSN
Volume Title
Publisher
Fen Bilimleri Enstitüsü
Abstract
A contact structure on a 3-manifold is a maximally non-integrable 2-plane field distributed
all over the 3-manifold. There are two types of contact structures on 3-manifolds:
tight and overtwisted. Knots that are everywhere tangent to the contact planes are called
Legendrian knots. In this thesis, we study basic techniques used in the classification
Legendrian knots. The aim of this thesis is to examine the techniques used in the classification
of Legendrian knots in tight contact manifolds and the techniques used in the
classification of Legendrian knots that have tight complements in overtwisted contact
manifolds. For this purpose, in this thesis we study the classification of Legendrian
unknots in contact 3-sphere S3 in detail.
Description
Citation
[1] Marinet J., Formes de contact sur les variétés de dimension 3, Proceedings of
Liverpool Singularities Symposium II Lecture Notes in Mathematics Volume 209,
142–163, 1971.
[2] Bennequin D., Entrelacements et équations de Pfaff, Astérisque, 107–108, 87–161,
1983.
[3] Eliashberg Y., Classification of overtwisted contact structures on 3-manifolds, Invent.
Math. 98, 623–637, 1989.
[4] Etnyre J. B., Honda K., On the nonexistence of tight contact structures, Annals
of Math. 153, 749–766, 2001.
[5] Eliashberg Y., Fraser M., Topologically trivial Legendrian knots, J. Symplectic
Geom., 7(2):77–127, 2009.
[6] Etnyre J. B., Honda K., Knots and contact geometry. I. Torus knots and the figure
eight knot., J. Symplectic Geom., 1(1):63–120, 2001.
[7] Geiges H., Onaran S., Legendrian rational unknots in lens spaces, J.Symplectic
Geom, Vol. 13, No. 1, 17–50, 2015.
[8] Baker K. L, Etnyre J. B., Rational linking and contact geometry, Progr. Math.
296 19–37, 2009.
[9] Ghiggini P., Linear Legendrian curves in T3, Math. Proc. Cambridge Philos. Soc.
140 , no. 3, 451–473, 2006.
[10] Geiges H., An introduction to contact topology, Cambridge studies in advanced
mathematics Vol.109, 2008.
[11] Etnyre, J. B., Introductory Lectures on Contact Geometry, In Topology and Geometry
of Manifolds, Athens, 81–107, 2001. Proceedings of Symposia in Pure
Mathematics 71. Providence, RI: American Mathematical Society, 2003.
[12] Etnyre J. B., Legendrian and transversal knots, Handbook of knot theory, 2005.
51
[13] McDuff D., Salamon D., Introduction to Symplectic Topology, Oxford University
Press, 1995.
[14] Rolfsen D., Knots and Links, Mathematics Lecture Series 7, Publish or Perish Inc,
1976.
[15] Adams C. C, The Knot Book: an elementary introduction to the mathematical
theory of knots, 2004.
[16] Ozbagci B., Stipsicz A. I., Surgery on contact 3-manifolds and Stein surfaces,
Bolyai Society Mathematical Studies, 2004.
[17] Giroux E., Convexité en topologie de contact, Comment. Math. Helv. 66, no. 4,
637–677, 1991.
[18] Honda K., On the classification of tight contact structures I, Geom. Topol. 4,
309–368, 2000.
[19] Saveliev N., Lectures on the topology of 3-manifolds: an introduction to the Casson
Invariant, Berlin; Newyork: De Gruyter, 1999.
[20] Kirby R. C., The topology of 4-manifolds, Springer Lecture Notes 1374, Springer-
Verlag 1989.
[21] Gompf R. E., Stipsicz A. I.,4-manifolds and Kirby calculus, Graduate Studies in
Mathematics, vol. 20, American Math. Society, Providence 1999.
[22] Lickorish R., A representation of orientable combinatorial 3-manifolds, Ann. of
Math. 76 , 531–540, 1962.
[23] Wallace A. H, Modifications and cobounding manifolds, Canad. J. Math. 12, 503–
528, 1960.
[24] Ding F., Geiges H., A Legendrian surgery presentation of contact 3-manifolds,
Math. Proc. Cambridge Philos. Soc. 136, 583–598, 2001.
[25] Ding F., Geiges H., Stipsicz A., Surgery diagrams for contact 3-manifolds, Turkish
J. Math. 28, 41–74, 2004.
52
[26] Gompf R. E., Handlebody construction of Stein surfaces, Ann. of Math. (2) 148 ,
619–693, 1998.
[27] Ding F., Geiges H., Symplectic fillability of tight contact structures on torus bundles,
Algebr. Geom. Topol. 1, 153–172, 2001.
[28] Dymara K. 2001, Legendrian knots in overtwisted contact structures on S3. Ann.
Global Anal. Geom., 19(3):293–305.
[29] Dymara K., Legendrian knots in overtwisted contact structures,
www.arxiv.org/abs/math.GT/0410122.
[30] J. B. Etnyre, On Contact Surgery, Proc. of the AMS, 136, no. 9, 3355–3362, 2008.
[31] Lisca P., Ozsváth P., Stipsicz A. I. , ve Szabó Z., Heegaard Floer invariants of
Legendrian knots in contact three-manifolds, J. Eur. Math. Soc. 11, no. 6, 1307–
1363. 2009.
[32] Plamenevskaya O., On Legendrian surgeries between lens spaces, J. Symplectic
Geom. 10, 165–181, 2012.