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Knot theory is dealing with embedding of curves in manifolds of dimension 3. A knot is a single circle embedded in the affine space of dimension 3 as a smooth curve not crossing itself. Many knot invariants are known and can be used to distinguish knots.

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How to show whether a given knot and its mirror image are the same or not?

Rigorous answer to this question is to use the Hemion's algorithm. See http://ukcatalogue.oup.com/product/9780198596974.do But it is complicated.
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Introductory article of knot Heegaard Floer Homology

I am looking for some article that gives an introduction to Heegaard Floer homology of knot. I heard that it is very useful to determine the unknotting number of a knot, but I couldn't find any intro …
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