Colored HOMFLY homology of rational tangles

Jake Rasmussen (University of Cambridge)

Monday 17th March, 2014 16:00-17:00 Maths 204


The \Lamba^k colored HOMFLY homology is an invariant of knots in S^3. It 
categorifies the sl(n) quantum invariant associated to the representation 
\Lambda^k(C^n) for n>>0. Gukov and Stosic conjectured that if K is a 
rational knot, the dimension of its \Lambda^k homology is the kth power of 
the dimension of the \Lambda^1 homology. I'll explain how to prove the 
analog of this conjecture for rational tangles and give a geometric 
interpretation of the tangle invariant which may seem familiar to those 
familiar with Heegaard Floer homology. Joint work with Mihajlo Cevic and 
Paul Wedrich.

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