Conjectures about virtual Legendrian knots and links

We formulate conjectures generalizing some known results to the category of virtual Legendrian knots. This includes statements relating virtual Legendrian knots to ordinary Legendrian knots, non-existence of positive virtual Legendrian self isotopies for the class of the fiber of ST⁎M and the conjec...

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Bibliographic Details
Published in:Journal of geometry and physics 2023-11, Vol.193, p.104962, Article 104962
Main Authors: Chernov, Vladimir, Sadykov, Rustam
Format: Article
Language:English
Subjects:
Causality
Legendrian knot
Linking
Low conjecture
Non-negative Legendrian isotopy
Positive Legendrian isotopy
Spacetime
Virtual knot
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Summary:We formulate conjectures generalizing some known results to the category of virtual Legendrian knots. This includes statements relating virtual Legendrian knots to ordinary Legendrian knots, non-existence of positive virtual Legendrian self isotopies for the class of the fiber of ST⁎M and the conjectural relation of virtual Legendrian isotopies to causality in generalized spacetimes. We prove the conjectures in the case of 2-dimensional M and (2+1)-dimensional spacetimes. We also formulate and prove the version of the Arnold's 4 cusp conjecture for virtual isotopies.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2023.104962