GI and Knot Problem both are problem of deciding structural equivalence of mathematical objects. Are there any results establishing connections between them? Nice connections of knot problem to statistical physics have been explored via knot polynomials, are there similar results for $GI$?
It would be particularly helpful to know if there are any standard results/warnings/suggestions/comments before one start looking into $GI$ motivated by knot problem. Actually, I was wondering if its recommended to explore in this direction for my master's thesis. I am interested in quantum/classical approaches to $GI$ and algebraic problems. Any other suggestions are welcome.