@RobertCardona: If you haven't figured it out already, I'll try to explain tomorrow. It's 1.30 am over here so I'm a bit too tired to write a good explanation. Have a good night!

It's 1:30 am here too :P

I haven't figured it out. I'm taking a break and setting up the server. Can't get DNS to work :/

Talk to you tomorrow.

I've got a mirror of the stacks project successfully running. I now just need to update both of my skeleton copies. I should have something up within a few hours. It has a nice commenting system! So for those who want to add, but don't know git or don't care for it, they can easily comment contribute anyway!

Don't count on it. I'm encountering some challenges. It may take some time.

You can check out my stacks mirror though.

I'm surprised the graphs work. It's going to look cool once I get it set up right.

Hopefully it encourages more people to participate in the reading group.

My only disappointment so far is that I'm spending far too much time coding instead of doing math :'(

I'm going to go get some lunch. I'll come back to it in an hour or two. I'll have the project done in a few hours. Probably by the time you wake up.

@RobertCardona $\mathbb{R}$-linearity comes into play because you take the multiplication by $g$ out of the differentiation. Matrix multiplication is nothing else than adding vectors and scaling some of them, so you can change order of matrix multiplication and differentiation. Write it down explicitly if you don't see why this is true.

@RobertCardona I guess then you don't really need Proposition 2 to see that $\left.\frac{d}{dt}\right|_{t = 0} c(t) = c'(0)$, but in general, $c: (a,b) \to M$ is not differentiable in the usual sense, so you need a chart as in Proposition 2 to make sense of the expression $c'(t)$.

I'm currently working on something else, but I think something of this form was proven in Lee: For $n \leq 3$, all topological $n$-manifolds are also smooth $n$-manifolds. Is there a fast argument for this?

hey @Mike

Hey. That's actually a really hard fact. The 2-simensional case is easier but still probably not worth reading; it's not far off from just classifying surfaces. I tried to read the 3-dimensional one once and found it too dense to get through.

(The smooth structures are actually also unique up to diffeo.)

ok, then it's not important. I figured if it's a simple argument, then I'd like to know it

Yeah, I gotcha. Worth knowing the fact, at least.

@Mike how come you're here and not in the main room?

Whim?

Ok.

@MikeMiller: I have an exercise: Let $\gamma_1, \gamma_2$ be two non-seperating curves on a cco surface $S$. Show that there exists a homeomorphism $f: S \to S$ with $f(\gamma_1) = \gamma_2$. Shouldn't these curves also be simple and closed?

Yeah. Authors probably thought that was implicit for whatever reason.

Anyone familiar with makefiles?

@RobertCardona: Try the TeX chat? :P

Figured it out! :)

This is all I was able to get: site. You can get the pdf or link to the git page, but you can't browse online.

I don't have time to investigate why it's not working. I've already spend the entire day debugging code. Can't do it again. If anyone sees why, let me know.

The problem is that all the tags are 'inactive' for some reason.