Geodesic
Single-Valued $q$-Differentials on Variable Finite Riemann Surface
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 3, pp. 50-61

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In present article are construction general theory of single-valued functions and $q$-differentials on variable finite Riemann surfaces begun. We constructed all form elementary $q$-differentials. We found dimensions and constructed explicit basis in important two factor spaces. In particular, we found dimension and constructed basis in first holomorphic cohomology group de Rham for 1-differentials.
Keywords: Teichmueller space of finite Riemann surfaces, $q$-differentials, vector bundles, Jacobi manifolds. 
@article{VNGU_2014_14_3_a4,
     author = {A. A. Kazanceva},
     title = {Single-Valued $q${-Differentials} on {Variable} {Finite} {Riemann} {Surface}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {50--61},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2014_14_3_a4/}
}
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A. A. Kazanceva. Single-Valued $q$-Differentials on Variable Finite Riemann Surface. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 3, pp. 50-61. http://geodesic.mathdoc.fr/item/VNGU_2014_14_3_a4/