Notes for AKT-090915/0:03:24: Difference between revisions

Latest revision as of 12:36, 30 August 2011

Review and additions to last class, corrections:

The Jones polynomial is usually normalized by diving by $\left\langle \bigcirc \right\rangle$ , the bracket of the unknot (i.e. dividing by an additional factor of $d$ ).
We can prove that for any knot $K$ , $J(K)$ is a polynomial of $A^{4}$ . Hence, we can substitute $A=q^{1/4}$ to get a Laurent polynomial in $q$ .

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 Review and additions to last class, corrections:
-# Jones polynomial is usually normalized by diving the '<>' of an unknot (i.e. divide by an additional factor of <math>d</math>).
+# The Jones polynomial is usually normalized by diving by <math>\left\langle \bigcirc \right\rangle</math>, the bracket of the unknot (i.e. dividing by an additional factor of <math>d</math>).
-# We can prove all knot <math>K</math> has <math>J(K)</math> being a polynomial of <math>A^4</math>, hence we substitute <math>A=q^{1/4}</math>.
+# We can prove that for any knot <math>K</math>, <math>J(K)</math> is a polynomial of <math>A^4</math>. Hence, we can substitute <math>A=q^{1/4}</math> to get a Laurent polynomial in <math>q</math>.