Legendrian Knots in Overtwisted Contact Structures on S3 |
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Authors: | Katarzyna Dymara |
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Institution: | (1) Instytut Matematyczny, Uniwersytet Wrocawski, Plac Grunwaldzki 2/4, 50-384 Wrocaw, Poland |
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Abstract: | We study the problem of classifying Legendrian knots in overtwisted contact structures on S
3. The question is whether topologically isotopic Legendrian knots have to be Legendrian isotopic if they have equal values of the well-known invariants rot and tb. We give positive answer in the case that there is an overtwisted disc intersecting none of the knots and we construct an example of a knot intersecting each overtwisted disc (this provides a counterexample to the conjecture of Eliashberg). Our proof needs some results on the structure of the group of contactomorphisms of S
3. We divide the subgroup Cont+(S
3, ) of coorientation-preserving contactomorphisms for an overtwisted contact distribution into two classes. |
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Keywords: | contactomorphism Legendrian knot overtwisted contact structure |
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