Abstract
We study the universal covering space $\tilde M$ of a holomorphic family (M, π, R) of Riemann surfaces over a Riemann surface R. The main result is that (1) $\tilde M$ is topologically equivalent to a two-dimensional cell, (2) $\tilde M$ is analytically equivalent to a bounded domain in C2, (3) $\tilde M$ is not analytically equivalent to the two-dimensional unit ball B2 under a certain condition, and (4) $\tilde M$ is analytically equivalent to the two-dimensional polydisc Δ2 if and only if the homotopic monodoromy group of (M, π, R) is finite.
Citation
Yoichi Imayoshi. Minori Nishimura. "A remark on universal coverings of holomorphic families of Riemann surfaces." Kodai Math. J. 28 (2) 230 - 247, June 2005. https://doi.org/10.2996/kmj/1123767005
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