2023/02/07 by Chernov, Vladimir, Sadykov, Rustam
#57D15 #83C75 #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Topology (math.GT) #Primary 53C24 #Secondary 53C50 #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2302.03607
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.