Lately I have been studying knot theory, I find it interesting. (I have also been studying Differential Equations, I am studing for the next semester as a math major.)
Anyway I have come up with my own knot invarient polynomial. It works really well in recognizing unknots (most of the time). However I have found a bothersome symmetry in how it shouldn't matter where your starting point and direction are. Because of this I have found that it isn't able to distingush between right-handed tri-foil knots & left-handed tri-foil knots, since with my equation, starting on the inside of a right-handed knot instead of the outside, or traveling in the oppisite direction from the starting, gives the same equation as if I 'mirror' the knot by flipping all of the crossovers with cross unders.
Does anybody here know anything about how to distingush right-handed knots and left-handed knots, using properties that do not change no matter how tangled up the knot is?
