Top-degree HOMFLY conjecture for arbitrary plabic graphs

Let GG be a plabic graph with c(G)\operatorname{c}(G) connected components and nn interior faces. Let LGplabL^{\operatorname{plab}}_G be its associated plabic graph link, and let \PtopL(q)\Ptop_L(q) be obtained from the top aa-degree term of its HOMFLY polynomial by the stated specialization. Top-degree HOMFLY conjecture.

degatopP(LGplab)=c(G)n1,\deg_a^{\operatorname{top}}P(L^{\operatorname{plab}}_G)=\operatorname{c}(G)-n-1, deg(\PtopL(q))=n,\deg(\Ptop_L(q))=n,

and the leading coefficient of \PtopL(q)\Ptop_L(q) is 11. This is presented as a basic extension beyond simple plabic graphs, including graphs with interior leaves. The supplied source gives no resolution status.

Sources & referencesView supporting material

Primary source

Pavel Galashin and Thomas Lam, “Plabic links, quivers, and skein relations”, arXiv:2208.01175 (2022).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.