Link invariants from quivers · Question 3
Cluster algebras and braid varieties · Historical workshop question
Problem statement
In high levels of generality, varieties pick up a mixed Hodge structure (Lam-Speyer). When the cluster variety is adequately nice, the mixed Hodge structure has only two dimensions, and the point count polynomial corresponds to a certain polynomial, but not the HOMFLY-PT.
What is the relationship between the mixed Hodge structure on the cohomology of a cluster variety coming from a plabic graph and knot invariants (eg. the Khovanov-Rozansky homology)?
Lean 4
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Historical workshop record. Current open/solved status has not been independently reassessed.
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- [1]Cluster algebras and braid varieties link
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