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Riemann surface

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I just finished typing in an entry on Riemann surfaces. It would really be nice to embellish it with illustrations of the Riemann surfaces of the square root function and the logarithm discussed in the entry.

I was wondering if someone might be interested in supplying some illustrations in a suitable format for inclusion in Planet Math. I know next to nothing about graphics programs and, most likely don't have the software needed to make the drawings. (and, if it's commercial, I wouldn't have the money to buy it --- my budget is about as low and tight as that of Planet Math :( )

Also, I was thinking of including some pictures of my paper models of Riemann surface. Can this be done? What file format would they have to be in and how and where to include them in Plante Math. (Since I don't have a digital camera at the moment and it might be a while before I get one due to the problems mentione in the comment to last paragraph. Nevertheless, it would be nice to know what to do with the pictures once I do get a camera.)

you need to load the graphicx package in order to use pictures (I think it's loaded by default).
If you want to use pictures on your entries, you need to upload them in EPS format using the "filebox" part of the enry editing dialog.

I can help you creating such graphics if you show me how these look
I'm training my pstricks skills right now so if possible, I would give you code to include them directly on code, but if it's too complicated I have many graphic programs that can output EPS and I would send the pictures back to you.

You just show me how they want to look and I'll create the drawings
(for these and any other entries you might want, I'd love to see PM to be much more graphical)
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

I think it should be change the "homomorphism" word to "homeomorphism", because homomorphism is applied when there is an algebraic operation involved in the domain of definition.

cf. http://en.wikipedia.org/wiki/Riemann_surface

thanks

I love Wikipedia, but you should always doublecheck with some other source before quoting it. In this case of the confusingly similar terms, I checked with Mathworld.

wikipedia (et al.) only corroborates what it is known from: Wells, Gunning, Griffiths and others... greets

I don't mean to come across as an anti-Wiki snob ;) but someone must've deleted the Wells, Gunning, Griffiths and others references from the WP article on homeomorphism. The WP article on homomorphism (or at least the version I'm looking at right now) has only one citation, for Burris & Sankappanavar.

I acknowledge this entry is not complete yet. A few other people besides myself have access to make changes. I call dibs on making graphics of a couple of the more famous Riemann surfaces with Mathematica.

Calling dibs is silly and immature. If someone has graphics
to contribute, that person should contribute graphics rather
than getting hung up bickering over priority. As time allows,
I wiill work on the part about the sheaf-theoretic approach to
Riemann surface theory.

I could've been criticized for not volunteering to do anything and leaving everything to others to do. Damned if you do, damned if you don't.

I see that I misunderstood what you were saying. I would be
quite glad to have you add figures. Also, maybe we could
make some attachments which give examples of Riemann surfaces,
such as the "famous Reimann surfaces' you mentioned earlier.

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