| Résume | Tropical vertex deals with automorphisms of the algebra of co,plex Laurent polynomials in two commuting variables with coefficients in the algebra of univariate formal series. One of the central problems in this theory is the computation of commutators of automorphisms. Gross-Pandharipande, and Siebert solved it expressing commutators of certain basic automorphisms via complex enumerative invariants of toric surfaces. Filippini and Stoppa extended this result to the case of non-commuting variables obtaining expressions with Block-Goettsche refined tropical invariants. We show that the above complex and refined invariants can be recovered from certain real enumerative invariants of toric surfaces. The idea can be traced back to Mikhalkin’s quantized real enumerative invariants. |
