Universität zu Köln

Geiges, Hansjorg and Onaran, Sinem (2020). Exceptional Legendrian Torus Knots. Int. Math. Res. Notices, 2020 (22). S. 8786 - 8818. OXFORD: OXFORD UNIV PRESS. ISSN 1687-0247

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Abstract

We present classification results for exceptional Legendrian realisations of torus knots. These are the first results of that kind for non-trivial topological knot types. Enumeration results of Ding-Li-Zhang concerning tight contact structures on certain Seifert fibred manifolds with boundary allow us to place upper bounds on the number of tight contact structures on the complements of torus knots; the classification of exceptional realisations of these torus knots is then achieved by exhibiting sufficiently many realisations in terms of contact surgery diagrams. We also discuss a couple of general theorems about the existence of exceptional Legendrian knots.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Geiges, Hansjorg UNSPECIFIED UNSPECIFIED UNSPECIFIED Onaran, Sinem UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-312705
DOI:	10.1093/imrn/rny253
Journal or Publication Title:	Int. Math. Res. Notices
Volume:	2020
Number:	22
Page Range:	S. 8786 - 8818
Date:	2020
Publisher:	OXFORD UNIV PRESS
Place of Publication:	OXFORD
ISSN:	1687-0247
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CONTACT STRUCTURES; SURGERY; INVARIANTS; LINKING Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/31270