Square-tiled tori
نویسندگان
چکیده
We study square-tiled tori, that is, tori obtained from a finite collection of unit squares by parallel side identifications. Square-tiled can be parametrized in natural way allows to count the number tiled given square tiles. There is $\mathrm{SL}(2,\mathbf{Z})$-action on and we classify $\mathrm{SL}(2,\mathbf{Z})$-orbits using two numerical invariants easily computed. deduce exact size every $\mathrm{SL}(2,\mathbf{Z})$-orbit. In particular, this answers question M. Bolognesi cyclic covers torus, which corresponds particular tori. also give asymptotic behavior
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2023
ISSN: ['1553-5231', '1078-0947']
DOI: https://doi.org/10.3934/dcds.2022185