Invariants of virtual knots? Which invariants of classical knots are known to extend to virtual ones? In literature I have only found the Alexander polynomial to be defined for virtual knots.
 A: Many (maybe most) classical invariants of knots extend to virtual knots, some in different ways.
Here are some examples.
In this paper it is shown that associated to any virtual link is a canonical one that lies in a thickened surface:
Kuperberg, Greg, What is a virtual link?, Algebr. Geom. Topol. 3, 587-591 (2003). ZBL1031.57010, MR1997331.
So one could define the fundamental group of a virtual link to be the fundamental group of the complement of the link in the thickened surface. This will agree with the notion of fundamental group if the link is classical (at least for knots, otherwise one has to be a bit careful with basepoints for split links). Another way one can define the fundamental group of a virtual link is to "kill" the peripheral subgroups in the thickened surface; again this will agree in the classical case when the surface is a 2-sphere.
The Jones polynomial and Khovanov homology have various extensions to virtual links. See e.g. this paper dealing with Khovanov homology for virtual links.
Also Kauffman's survey.
See this seminar series for several talks about virtual knots.
