The knot up there is called trefoil. You will certainly be
happy to know that its Alexander polynomial is t2 - t + 1, and you
will be delighted from the fact that the Seiberg-Witten invariant of its 0-surgery
equals 1, in correspondence of the trivial class. I don't
forget to reassure you that it is moreover a fibered knot (something that
you certainly have noticed if you own a 3D browser).
To obtain the same data for Sylvester The Cat requires more work
(especially if the cat goes on moving). Getting to know
this data is the main purpose of my research. This is why I study math.