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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? 
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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!



Links which HOMFLY homology distinguish but the HOMFLY polynomial does not.
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](http://arxiv.org/abs/1211.6075) by Gukov-Saberi.)


In addition, some mutant pairs can be distinguished by Khovanov homology. (See the [paper](http://xxx.lanl.gov/pdf/math/0301312v1.pdf) by Wehrli.)


