  Block and G\"ottsche have defined a $q$-number refinement of counts of
tropical curves in $\mathbb{R}^2$. Under the change of variables $q=e^{iu}$, we
show that the result is a generating series of higher genus log Gromov-Witten
invariants with insertion of a lambda class. This gives a geometric
interpretation of the Block-G\"ottsche invariants and makes their deformation
invariance manifest.

Algebraic Geometry