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arxiv: 0806.1705 · v1 · submitted 2008-06-10 · 🧮 math.DS

Schottky groups cannot act on mathbb{P}^(2n)_{mathbb{C}} as subgroups of PSL(2n+1,Bbb{C})

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keywords groupsschottkysubgroupscannotmathbbbasiccalleddevelop
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In this paper we look at a special type of discrete subgroups of $PSL_{n+1}(\Bbb{C})$ called Schottky groups. We develop some basic properties of these groups and their limit set when $n > 1$, and we prove that Schottky groups only occur in odd dimensions, {\it i.e.}, they cannot be realized as subgroups of $PSL_{2n+1}(\Bbb{C})$.

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