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Topological invariants of some chemical reaction networks

Certain toric dynamical systems studied in physical chemistry have associated toric varieties which, when smooth, represent elements in the homotopy groups $Mξ_*B\T$ of a symplectic variant of the $A_\infty$ Baker-Richter spectrum $Mξ$. The noncommutative Hopf algebroid $(Mξ_*,Mξ_*Mξ)$ has interesting connections to the group of formal diffeomorphism of the noncommutative line, conjecturally defining a noncommutative analog Helmholtz free energy for systems of complex symplectic (completely integrable) Hamiltonian toric manifolds