Oh... if its taking the conjugate of a fixed point , that actually makes sense and clears up so much confusion. But that is not what my book says which is why I'm confused. Perhaps you can take a look at what the author is saying and you will understand what he means and where I'm going wrong...
just in case anyone ever sees this, I think* I figured out why z* is listed as a Mobius transformation. Because think of this, Mobius transformations are mappings T(z):C* --> C* (where C* is the extended complex plane). We know that the extended complex plane is isomorphic to the Reimann...
Hi guys,
I am having a very stupid problem. I can't figure out what Mobius transformation represents T(z)=z*, where z* is the complex conjugate of z.
In my book we are learning about Mobius transformations and how they represent the group of automorphisms of the extended complex plane (Ʃ). [...
thank you for the reply. Yes I have been wrecking my brain trying to understand triangulation. It sounds simple but (to me) it's not. I guess I just need to keep reading and will look to understanding simplical complexes first. What was really confusing me was why you have to have a minimum...
I'm sorry I should have been specific. Yes I was speaking of a closed, compact surface (connected 2-manifold). All the theorems I see regarding this are that you can represent a compact surface by an even sided polygon. And it was my impression that to triangulate a compact surface each...
EDIT: My guess to the below question is that no you can't triangulate a triangle because a legitimate triangulation each edge can only be linked up to exactly two distinct faces, so if you just have one triangle, each edge would be linked up to one face (the face of the triangle)
I'm really...
I know that open intervals in R are homeomorphic to R. But does this extend to any dimension of Euclidean space? (Like an open 4-ball is it homeomorphic to R^4?)
My book doesn't talk about anything general like that and only gives examples from R^2.
Say we have a disconnected manifold with components C1, C2, C3. (I know in the threat title I said just topological space, but I'm actually thinking of manifolds here, sorry! Not sure how to change the title) It makes intuitive sense that if we're looking at just one of the components, then...
hey kreizhn, thank you very much this is a detailed response and helps a lot. I kept getting hung up on the fact that there were no edge labelings that would tell me what to "glue together" as in the examples of the square for the torous and klein bottle. But I guess I was completely...
I have one other question and I'd appreciate any insight in to. What exactly is "homeomorphism type"? I understand well what a homeomorphism is, but not what a homeomorphism type is. For example, I read about lens spaces and read things like "some lens spaces have the same homotopy type but...
Hello, I have been given a homework problem and I don't want any help on solving the problem, (I'm not even going to post the problem - I want to figure it out myself), I only want to understand what the problem is asking. (That's why I've posted in this section rather than the homework...