Augusto Matteini

Does anyone know a good text reference for fuchsian and quasi-fuchsian group? I'm interested in the basics for studying Teichmuller theory, I found the handbook of Papadopoulos but they seems a little bit overwhelming for a start

Does anyone know how does he conclude with the implicit map theorem? I don't understand why g has to be equal to f. After that it is clear but I don't understand neither how does he know that it should have g(y)=f(y) neither why the condition implies the equality of the 2 functions thank you.

It's just that Heine Borel is such a way of life that as soon as i saw open and compact it had to be "him" haha

Thank you

saying that being compact means closed and limited is a contraddiction to being open and compact only if i use that the only clopen set in Rn is Rn itself

yeah that was dumb lol you are right

In all the answers that I fount related to submersion of compact manifold in $R^{n}$ they always conclude using connection of $R^{n}$ (ie math.stackexchange.com/questions/1995022/…) Now, while of course it does not change much, would it be wrong arguing that f(M) must be compact and open but this is against Heine Borel?

(Of course I could prove that the torus is compact as closed and limited, product of compact... but I'm interested if I'm doing something missleading when dealing with equivalence class)

When i view the torus as $\mathbb{R}^{2}/\langle(x+1,y),(x,y+1)\rangle$ can i just say that it is compact using that the restriction of the projection to $[0,1]\times[0,1]$ is surjective and continuous? The morale of this is that it is a fundamental domain but I don't really need it for a "weak" argument related to just compacteness, do I?

you wrote it yourself

Friends lie, Girlfriends lie, Algebra does not

in that case you can have more than 1 answers only if sqrt(b)=-sqrt(b) as you wrote hence b=0

that thing is 0 because a=sqrt(b) but you already know that, it's literally your first line

you can't assume that from what you have wrote

the "from this" we can say it's just false

@user123456789 Just ask; don't ask to ask

I can use the classic Cauchy-inequality to prove the theorem but I would like to understand from where that integral cames up

I can just "copy" the proof that the coefficient of a Fourier series are in that form and adapt it to Homogeneus Expansion for holomorphic function?

Any hint on how to prove the following integral equality? I'm getting lost because it seems to me that we are mixing some Cauchy integral formula with some Fourier Series but I've never seen anything similar in class

ok im dumb, p* is always injective

Or if it is not that how can i obtain a surjective homomorphism from $H$ having one from $C$? For how it is left is should be trivial but I could not find any argument

thank you in advance

Could anyone try to help me understand why in the proof of theorem 3.2 page 13 (here numdam.org/item/10.5802/aif.2098.pdf) is it so obvious that $\pi_{1}(C)\simeq H$? For what I have understood it should be $p*(\pi_{1}(C))\simeq H$

@leslietownes a bless in disguise

Hi, a little group theory problem i got stuck all day and cant seem to be able to solve it. I have a group and i'm supposing that it is left orderable. If I know that $yhy^{-1}=h^{-1}$ and that $h^{-k}<y^{2}<h^k$ and $h^{-k}<y^{-2}<h^{k}$ with $h>1, k>0$ how can I show that $yhy^{-1}>1$? I've tried for a while to work it out with "bare hands calculation" but I think I'm missing something

@BalarkaSen I agree

This is what you meant right? mathcurve.com/surfaces.gb/seifert/seifert.shtml

Hi @BalarkaSen, no never seen a Siefert surface of the trefoil knot?

while Munkres is "too easy"

but I only know hatcher from Algebraic Topology and his 3-manifold notes are quite an advanced starting point (at least for my pov) and don't even cover this topic

I mean if you have any reference book I will be delighted to stop bothering you

when it gets in technicality I agree that I don't have the backround but I was more interested in the algebraic flavour of the paper

Some parts, I don't have the arrogance to say that I'm good in 3-manifolds

But it's just an example

I don't have the appropriate background to work out the example alone

It's an example in a paper

I wish i knew some topologist haha

what is a meridional slope? is it a circle? half a circle? I literally never heard of it, only heard of slope for a line

last question I guess

Ok, sorry

Is this what they mean?

I was trying to understand the following example from a paper

I will repost something that i had already asked but I can't work it out alone, sorry

english is not my mother tangue and I've always encountered slope as in a line or a mountain, I would not know what use I should make of meridional slope

Or meridional slope is just the whole circle? I'm not sure about the wording "slope"

At least they intersect once I guess..