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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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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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  • $\begingroup$ This was exactly what I was looking for, thanks! $\endgroup$
    – Michael Abel
    Commented Apr 29, 2013 at 17:58
  • $\begingroup$ However, the colored Jones polynomials do distinguish the $5_1$ and $10_132$ knots (according to the Knot Atlast). $\endgroup$
    – Peter Samuelson
    Commented Jul 19, 2013 at 5:34

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