Talk:Teichmüller space

I've started developing the article on this topic. I'm fairly new to the subject, however, and I've only seen a limited number of presentations of the material. I'd like suggestions (and contributions, of course) on making this article as accessible and useful as possible. JPB 04:03, 4 September 2005 (UTC)

In the line "... surface X (or its underlying topological structure) provides a marking X → Y of each Riemann surface Y represented in TX..." perhaps there is a link you can give to help me understand what you mean by marking. Dewa (talk) 19:28, 13 May 2008 (UTC)

Should add Beltrami coefficient to define Teichmuller spacec as B(X)_1/Diff_0(X) Wolfraine (talk) 10:55, 6 December 2009 (UTC)

Perhaps it would be helpful if the page included a definition. --70.233.154.17 (talk) 00:47, 13 March 2010 (UTC)

Annulus?

If you remove from the sphere two simply connected domains, you get something conformally equivalent to an annulus. So, these things, up to conformal equivalence, are characterized by the conformal modulus of the annulus, one real parameter. The article seems to say the Teichmuller space is infinite complex dimensional, because we have disks removed, pieces of ideal boundary. But these conformal equivalences seem to be isotopic to the identity... so, I'm not sure what the reason is for the difference between one real and infinite complex dimensions. Maybe some silly convention about fixing the maps on the boundary pieces? And, assuming the Teichmuller space is indeed considered infinite dim, is the space of annuli up to conformal equivalence a well-established space? Say, the moduli space of complex annuli, or I don't know how to call this? The moduli space article is not very readable for me, unfortunately. --GaborPete (talk) 08:23, 24 February 2010 (UTC)