Isomorphism between sutured monopole and sutured Floer contact invariants

Let (M,Γ,ξ)(M,\Gamma,\xi) be a sutured contact manifold, and let ψ(M,Γ,ξ)SHM(M,Γ)\psi(M,\Gamma,\xi)\in\underline{SHM}(-M,-\Gamma) and EH(M,Γ,ξ)SFH(M,Γ)EH(M,\Gamma,\xi)\in SFH(-M,-\Gamma) denote the monopole Floer and sutured Floer contact invariants, respectively. Let R\mathcal{R} be the coefficient ring used for sutured monopole Floer homology. Contact-invariant comparison conjecture. There exists an isomorphism

SHM(M,Γ)SFH(M,Γ)R\underline{SHM}(-M,-\Gamma)\longrightarrow SFH(-M,-\Gamma)\otimes\mathcal{R}

which sends ψ(M,Γ,ξ)\psi(M,\Gamma,\xi) to EH(M,Γ,ξ)1EH(M,\Gamma,\xi)\otimes 1. Such an isomorphism would identify the monopole and sutured Floer contact invariants and provide the anticipated agreement between the two contact theories. The source presents this as a future goal and gives no evidence of resolution.

Sources & referencesView supporting material

Primary source

John A. Baldwin and Steven Sivek, “A contact invariant in sutured monopole homology”, arXiv:1403.1930 (2014).

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.