Mathematics Stack Exchange
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Questions tagged [knot-invariants]

For properties of knots that remain unaffected by Reidemeister moves

Proving that two knots are not the same by proving that there is no injective homotopy from a knot to another is normally quite hard. Fortunately there are some properties of knot projections that remain invariant by Reidemeister moves, thus two knots with different invariants cannot be equivalent.

This tag is for questions concerning said properties.

323 questions
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Classification of knots with unknotting number 1.

Is there a classification of knots with unknotting number=1? I can think of one infinite family at least. That is, twist the unknot $n$ times then join the two ends together. In fact, I think maybe one could twist the unknot into a string and join…
zooby
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Computing Incorrect Signs for Planar Graph of an Alternating Knot Projection

I'm trying to work through the The Knot Book by Colin Adams, and I seem to be consistently coming up with edges for a planar graph of the figure-eight knot where there are both positive and negative edges. My method for determining the sign of those…
Chib
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