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

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+Review and additions to last class, corrections:
-Review and additions to last class, corrections: 1. Jones polynomial is usually normalized by diving the '<>' of an unknot (i.e. divide by an additional factor of d)  2.We can prove all knot K has J(K) being a polynomial of A^4, hence we substitute A=q^{1/4}
+# 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 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>.