Domino tilings on orientable surfaces (Q1268722)

\textit{J. H. Conway} and \textit{J. C. Lagarias} [J. Comb. Theory, Ser. A 53, No. 8, 183-208 (1990; Zbl 0741.05019)] and \textit{W. P. Thurston} [Am. Math. Mon. 97, No. 8, 757-773 (1990; Zbl 0714.52007)], using combinatorial group theory, give necessary and sufficient conditions for a simply-connected region of a checkerboard to be tiled by dominoes. The paper under review considers domino tiling of checkerboard-like orientable surfaces (possibly with boundary). Ito gives necessary and sufficient conditions, in terms of certain admissible null-homologous closed edge paths, for such a surface to be tiled by dominoes.