Ok, so this relates to my homework, but I really can't find an answer anywhere, so this is more of a general question. First off, what does a "chart" of a manifold look like? Is it a set, a function, a drawing, a table, what?! I have found so many things about charts, but nothing shows what they actually look like (either that or I am just not recognizing them). Secondly, using stereographical projection, what are the 4 charts of a torus? I saw something that looked something like(adsbygoogle = window.adsbygoogle || []).push({});

x^{1}= ((cosΘ, sinΘ), (cosφ, sinφ))= Θ

x^{2}= ((cosΘ, sinΘ), (cosφ, sinφ))= φ

and the other charts are similar. Would the other charts just be

y^{1}= ((cosΘ, sinΘ), (cosφ, sinφ))= Θ

y^{2}= ((cosΘ, sinΘ), (cosφ, sinφ))= φ

I'm just really confused on this topic and I would like to gain a little more confidence before going into my final. Are the "charts" that I gave actually charts, and are they the ones that describe a torus?

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# Charts of a torus (and other manifolds)

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