I have seen the definition of the Kauffman bracket of a link diagram and I understand that I could compute this polynomial $\langle D\rangle$ for a given diagram $D$ by choosing an ordering of the crossings of my diagram and then by applying the definition. However, I do not understand why the resulting polynomial does not depend on the ordering of the crossings that I have chosen?
Why is the Kauffman bracket well defined?
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algebraic-topology
knot-theory
low-dimensional-topology
knot-invariants
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0Have you seen the state-sum definition? – 2017-01-13
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0@AkivaWeinberger Yeah that is the definition that I have seen – 2017-01-13
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1Page 53 of [these notes](http://math.ucsd.edu/~justin/Roberts-Knotes-Jan2015.pdf) deals with making sure it's well-defined – 2017-01-13
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0@AkivaWeinberger Thanks - that is just what I needed! – 2017-01-13