Hostname: page-component-6587cd75c8-9kljr Total loading time: 0 Render date: 2025-04-23T20:25:05.606Z Has data issue: false hasContentIssue false

Strongly exceptional Legendrian connected sum of two Hopf links

Published online by Cambridge University Press:  10 December 2024

Youlin Li*
Affiliation:
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
Sinem Onaran
Affiliation:
Department of Mathematics, Hacettepe University, 06800 Beytepe-Ankara, Turkey e-mail: [email protected]

Abstract

In this paper, we give a complete coarse classification of strongly exceptional Legendrian realizations of the connected sum of two Hopf links in contact 3-spheres. This is the first classification result about exceptional Legendrian representatives for connected sums of link families.

Type
Article
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Dalton, J., Etnyre, J. and Traynor, L., Legendrian Torus and Cable Links, J. Symplectic Geom. 22(2024), no. 1, 11108.Google Scholar
Ding, F. and Geiges, H., Legendrian knots and links classified by classical invariants . Commun. Contemp. Math. 9(2007), 135162.CrossRefGoogle Scholar
Ding, F. and Geiges, H., Legendrian helix and cable links . Commun. Contemp. Math. 12(2010), 487500.CrossRefGoogle Scholar
Ding, F., Geiges, H. and Stipsicz, A. I., Surgery diagrams for contact 3-manifolds . Turkish J. Math. 28(2004), no. 1, 4174.Google Scholar
Dymara, K., Legendrian knots in overtwisted contact structures on ${S}^3$ . Ann. Global Anal. Geom. 19(2001), no. 3, 293305.CrossRefGoogle Scholar
Eliashberg, Y. and Fraser, M., Classification of topologically trivial Legendrian knots . In Geometry, topology, and dynamics (Montreal, PQ, 1995), CRM Proc. Lecture Notes, Vol. 15, Amer. Math. Soc., Providence, RI, 1998, 1751.Google Scholar
Etnyre, J. B., On knots in overtwisted contact structures . Quantum Topol. 4(2013), no. 3, 229264.CrossRefGoogle Scholar
Etnyre, J. B. and Honda, K., On connected sums and Legendrian knots . Adv. Math. 179(2003), no. 1, 5974.CrossRefGoogle Scholar
Etnyre, J., Min, H. and Mukherjee, A., Non-loose torus knots. Preprint, 2022, arXiv: 2206.14848.Google Scholar
Geiges, H. and Onaran, S., Legendrian rational unknots in lens spaces . J. Symplectic Geom. 13(2015), no. 1, 1750.CrossRefGoogle Scholar
Geiges, H. and Onaran, S., Legendrian Hopf links . Q. J. Math. 71(2020), no. 4, 14191459.CrossRefGoogle Scholar
Geiges, H. and Onaran, S., Exceptional Legendrian torus knots . Int. Math. Res. Not. IMRN (2020), no. 22, 87868817.Google Scholar
Honda, K., On the classification of tight contact structures . I. Geom. Topol. 4(2000), 309368.CrossRefGoogle Scholar
Honda, K., On the classification of tight contact structures II. J. Differential Geom. 55(2000), no. 1, 83143.CrossRefGoogle Scholar
Lisca, P., Ozsváth, P., Stipsicz, A. and Szabó, Z., Heegaard Floer invariants of Legendrian knots in contact three-manifolds . J. Eur. Math. Soc. (JEMS) 11(2009), no. 6, 13071363.CrossRefGoogle Scholar
Matkovic, I., Non-loose negative torus knots . Quantum Topol. 13(2022), no. 4, 669689.CrossRefGoogle Scholar
Wand, A., Tightness is preserved by Legendrian surgery . Ann. of Math. (2) 182(2015), no. 2, 723738.CrossRefGoogle Scholar
Wu, H., Legendrian vertical circles in small Seifert spaces . Commun. Contemp. Math. 8(2006), no. 2, 219246.CrossRefGoogle Scholar