We prove that for a parabolic subgroup of the fixed points sets of all elements in are the same. This result, together with a deep study of the structure of subgroups of acting freely and properly discontinuously on , entails a generalization of the so called weak Hurwitz’s theorem: namely that, given a complex manifold covered by and such that the group of deck transformations of the covering is “sufficiently generic”, then is isolated in .
@article{ASNSP_2002_5_1_4_851_0, author = {De Fabritiis, Chiara}, title = {Generic subgroups of Aut $\mathbb {B}^n$}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {851--868}, publisher = {Scuola normale superiore}, volume = {Ser. 5, 1}, number = {4}, year = {2002}, zbl = {pre02217022}, mrnumber = {1991005}, language = {en}, url = {archive.numdam.org/item/ASNSP_2002_5_1_4_851_0/} }
de Fabritiis, Chiara. Generic subgroups of Aut $\mathbb {B}^n$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 4, pp. 851-868. http://archive.numdam.org/item/ASNSP_2002_5_1_4_851_0/
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