The wheeling conjecture for Chinese-character diagram products

Let B{\mathcal B}' be the completed graded space of Chinese characters, equipped with the disjoint-union product and a second product transported from the diagram algebra via the isomorphism χ\chi. Let Ω\Omega be the wheels series and let Ω^:BB\hat{\Omega}:{\mathcal B}'\to{\mathcal B}' be the wheeling operator obtained by gluing all legs of the Chinese characters occurring in Ω\Omega to legs of an input diagram. Denote the two products by \mathaccent\mathaccent\cdot\cup and ×\times, respectively.

Wheeling conjecture. Wheeling intertwines the two products on Chinese characters; more precisely,

Ω^:(B,\mathaccent)(B,×)\hat{\Omega}:({\mathcal B}',\mathaccent\cdot\cup)\to({\mathcal B}',\times)

is an algebra isomorphism.

The conjecture is presented as a diagrammatic analogue of the Duflo isomorphism and is attributed in the source to an independent conjecture of Deligne. The supplied text does not establish whether it has been resolved.

Sources & referencesView supporting material

Primary source

Dror Bar-Natan, Stavros Garoufalidis, Lev Rozansky and Dylan P. Thurston, “Wheels, Wheeling, and the Kontsevich Integral of the Unknot”, arXiv:q-alg/9703025 (1998).

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.