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

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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>.

Latest revision as of 13:36, 30 August 2011

Review and additions to last class, corrections:

  1. The Jones polynomial is usually normalized by diving by , the bracket of the unknot (i.e. dividing by an additional factor of ).
  2. We can prove that for any knot , is a polynomial of . Hence, we can substitute to get a Laurent polynomial in .