The Jones Polynomial, Khovanov Homology, and Link Mutation -- Jonathan Bloom
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The Jones polynomial is an invariant of knots and, more generally, links. 
Mutation is a subtle way to change a link, and it is easy to see that mutant links have
the same Jones polynomial.   Khovanov homology is a strictly stronger invariant of links
which takes the form of a bigraded Abelian group.  I'll describe these notions,
emphasizing simple examples, and prove that mutant links have  the same Khovanov homology
as well (with coefficients in Z/2Z).  The integer coefficient case remains an open
problem, for more details see: <br/><A HREF="http://arxiv.org/abs/0903.3746" target="_self">http://arxiv.org/abs/0903.3746</A>
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Prerequisites: The first half should be accessible to everyone.  For the second half, I
will assume familiarity with groups/rings and their quotients (though over Z/2Z, this is
really linear algebra).