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10 votes
1 answer
442 views

Analytic continuation gives a covering space (and not just a local homeomorphism)

Let $\mathcal{G}$ be the space of germs of holomorphic functions defined on open subsets of $\mathbb{C}$, topologized in the usual way. There is a natural map $p\colon \mathcal{G} \rightarrow \mathbb{...
Paul's user avatar
  • 111
8 votes
2 answers
328 views

Equivalence of definitions of quasiconformal surfaces?

I have been reading John H. Hubbard's book Teichmüller Theory vol. 1 and I am a little bit concerned with his definition of quasiconformal surface. Definition: A quasiconformal surface $S$ is a ...
Maxime Scott's user avatar
4 votes
1 answer
172 views

Is every Cantor set $C\subseteq\mathbb R^{\infty}$ the limit set of a Fuchsian group?

Is every Cantor set $C\subseteq\mathbb R^{\infty}$ the limit set of a Fuchsian group? Let's recall the definitions. A Fuchsian group $G$ is a discrete subgroup of $\operatorname{PSL}(2,\mathbb R)=\...
Christian Remling's user avatar