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Does anyone know of a pair of different links which the HOMFLY polynomial does not distinguish, but HOMFLY homology does? Or does there exist such a pair of links?

I'm assuming there does exist such a pair, but have never seen it. I've been looking for this for a few days and have had no luck finding or computing such an example. Any help would be greatly appreciated!

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A related question is mathoverflow.net/questions/25747/… –  Gerry Myerson Apr 30 '13 at 5:08
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1 Answer

up vote 9 down vote accepted

Although $5_1$ and $10_{132}$ cannot be distinguished by Jones, Alexander and (uncolored) HOMFLY-PT polynomials, their HOMFLY homologies do tell them. (See the review by Gukov-Saberi.)

In addition, some mutant pairs can be distinguished by Khovanov homology. (See the paper by Wehrli.)

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This was exactly what I was looking for, thanks! –  Michael Abel Apr 29 '13 at 17:58
    
However, the colored Jones polynomials do distinguish the $5_1$ and $10_132$ knots (according to the Knot Atlast). –  Peter Samuelson Jul 19 '13 at 5:34
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