Abstract
The main result of this article is a Pfaffian formula for the partition function of the dimer model on any graph Γ embedded in a closed, possibly non-orientable surface Σ. This formula is suitable for computational purposes, and it is obtained using purely geometrical methods. The key step in the proof consists of a correspondence between some orientations on Γ and the set of pin− structures on Σ. This generalizes (and simplifies) the results of a previous article (Cimasoni and Reshetikhin in Commun Math Phys 275:187–208, 2007).
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