Conjectures about virtual Legendrian knots and links

Vladimir Chernov; Rustam Sadykov

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arXiv · 2302.03607

Conjectures about virtual Legendrian knots and links

Vladimir Chernov·Rustam Sadykov

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Abstract

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 isotopy for the class of the fiber of $ST^*M$ and the conjectural relation of virtual Legendrian isotopy 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.

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BibTeX RIS

Vladimir Chernov, Rustam Sadykov. 2023-02-07. Conjectures about virtual Legendrian knots and links. https://arxiv.org/abs/2302.03607

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