The closed-foam evaluation conjecture for instanton homology

Let Σ\Sigma be a closed foam in R3\R^{3}, and let SS be its underlying closed pre-foam. Let \Jsharp(Σ)\Jsharp(\Sigma) denote the instanton-homological evaluation of Σ\Sigma, and let \Jflat(S)\F\Jflat(S)\in\F be the evaluation defined by the proposed pre-foam rules. The closed-foam evaluation conjecture. For every such closed foam,

\Jsharp(Σ)=\Jflat(S).\Jsharp(\Sigma)=\Jflat(S).

This conjecture would identify the instanton-homological evaluation of closed foams with the combinatorial pre-foam evaluation. It is presented as one of two plausible conjectures arising from the unresolved well-definedness issue, and no proof or disproof is given in the supplied text.

Sources & referencesView supporting material

Primary source

P. B. Kronheimer and T. S. Mrowka, “Tait colorings, and an instanton homology for webs and foams”, arXiv:1508.07205 (2015).

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