I don't care if you read it for your own good. I care that if there's a question posed in the chat, and other people respond, you should read their responses before giving your own.
Presumably when he said 'minus open discs' he meant them to be small enough that the resulting space is a surface, so any covers of that are automatically surfaces.
hmm. that's interesting, I don't know of such a "good cover" off-hand. let me scroll on to see what you and PVAL discussed about branched covers (I've never grokked these)
Like you said, finite index subgroups give finite degree covers. It remains to figure out what the genus of these covers are and what the number of boundary components are. (And then once you have that, to draw the picture.)
seems nontrivial. btdubs, anon's questions seems to be answered by looking at the classical picture : $\Sigma_3$ covers $\Sigma_2$. so similarly, $\Sigma_{3, 2}$ should cover $\Sigma_{2, 1}$. or am I being silly?
i.e., take three torii squashed togather with two punctures at the end torii, and act by Z_2 using rotational symmetry
I guess it makes sense to think about branched covers. Those are precisely covers of $S^2$ minus $n$ punctures. But there's a whole load of rich theory about Riemann surfaces, and I don't know if something purely topological can be done.
seems like it has been pretty well-answered. i don't know the answer to the genus-of-covering question, though.
apologies for re-answering (even though my answer wasn't the one desired for)
@MikeMiller if I haven't told you already, I learnt what Bass-Serre theory is a few days ago from prof. seems pretty cool, although I don't know what it's used for.
ohh. whoa, I didn't know you can solve that for Gromov hyperbolic groups.
from what I understood from Bass-Serre theory, it's a nice way to visualize universal cover of spaces with fundamental group isomorphic to free product with amalgations. in case of $X \vee Y$, say (where the $\pi_1$ is just free product with no amalgation), the universal cover is a copy of $\tilde{X}$ stuck at each point of $\tilde{Y}$ corresponding to lifts of loops at $Y$ w/ some basept.
similar picture can be obtained for the general amalgated case, in which the resulting spaces is called the Bass-Serre tree.
for the amalgated case, you need something like a notion of an "edge space", which are intervals in the no-amalgation case. this is precisely $K(C, 1)$, where $C$ is the amalgation in the fundamental group of the total space.
I wish there was an "Approve edit with gusto" button. I can tell someone they suck when declining an edit, but I can't thank someone on behalf of the English language.
@Chris'ssistheartist i use large size papers pasted to the wall of my room when i concieve sophisticated graphs and equations for my projects that i do sketch them upon, try to do that its helpful ...... unless you have a memory of an elephant :D
hello i need some help with one problem , i have this 104,04$ on my account i know the Interest per year are 2% i need to know the started money 104,04 is about 2 years
Hi, can someone tell me how the author gets (13.17) from the previous two inequalities on p. 391 of math.ucdavis.edu/~hunter/book/ch13.pdf ? Note that the t in the second inequality is in (-1,0), which he left out.
