The h Bar

@0celo7 are test functions ideals of the smooth function ring

skullpatrol

2:19 PM

...or an exam?

[] can't seeyou :P:P::P (Hall of Mirrors)

"Fix a smooth derivative operator $\nabla_m$. For $g_{ab}$ a smooth metric, its curvature tensor ${R_{abc}}^d$ can be written $${R_{abc}}^d = {\rho_{abc}}^d - 2 {\Gamma^d}_{m[a} {\Gamma^m}_{b]c} - 2 \nabla_{[a} {\Gamma^d}_{b]c}$$ where $${\Gamma^a}_{bc} = \frac 12 g^{am} (2 \nabla_{(b} g_{c)m} - \nabla_m g_{bc})$$ and ${\rho_{abc}}^d$ is the curvature tensor of $\nabla_m$."

What

The hell is this

what connection, does not look levi citiva to me

Not a clue

bolbteppa

Looks like a non-Levi-Civita connection with non-partial derivative Christoffels?

2:34 PM

I suspect it's supposed to be a generic connection and the second term is supposed to remove all the non-metric part?

I dunno

@Slereah test functions form an algebra

are they an ideal of smooth function, though

yes

Good

@BalarkaSen what I don't understand is how the coarse equivalence class contains any information

2:39 PM

@0celo7 R^2 and R are not coarse equivalent

So it certainly contains some information

More precisely it keeps track of the "end space"

since when are you an expert

I hang out with a lot of geometric group theorists

nerd

certainly not an expert

how does a high schooler hang out with geometric group theorists

2:41 PM

with gusto

do they ever haze you

@BalarkaSen well tell me why anyone should give a shit about the Milnor-Svarc theorem

It give you examples of a LOT of Gromov hyperbolic groups

Any group which acts by isometries cocompactly and properly discontinuously on a negatively curved manifold is Gromov hyperbolic

If $M$ is negatively curved and compact, $\pi_1(M)$ is Gromov hyperbolic

I don't care about things just because they have a famous name attached

well if you dont care about gromov hyperbolic groups you shouldnt care about Milnor-Svarc theorem

2:43 PM

ok, good

::tosses book aside::

time to make some food

i need to decide what to do

Q: How to address high volume of low quality questions?

Ah, apparently $\nabla_m$ is indeed not a metric compatible connection

He defines it later on

I think it's not even supposed to be a connection

Just a very general derivative

Physics Meta

0

I've noticed that there are an awful lot of people who come here, create new accounts to ask their homework questions, get downvoted and closed then leave. Obviously, we have flags, we can attempt to edit and we can vote to show that they ARE not suited for physics SE, but I'm concerned that n...

"Let $S$ be a submanifold of dimension $d$ of the $n$-dimensional manifold $M$. Let $\alpha$ be a non-zero tensor distribution which has support on $S$ and is the sum of one distribution arising from a locally integrable tensor field and another the derivative of a distribution arising from a locally square-integrable field. Then $d = n-1$"

Sir Cumference

@JohnRennie Obviously I don't want to regurgitate the information, I want to learn the material. But the cost of university is insane if it's goal is merely to "provide guidance" to information we'll be teaching ourselves anyway.

Anonymous

2:55 PM

@SirCumference That is a reasonable argument, considering the cost of education in the US :P

hmm... it seems the quantum guys are quite busy, danialsank is not frequently on as in the past. Guess most end up doing software stuff

There's a counterargument there somewhere along the lines of, merely reading textbooks cannot communicate the basic scientific "intuitions" that is essential to research in every field of science. But I am not qualified enough to actually pose that as a counterargument.

(I want to say the same for emilo, but well, he is on in recent days quite frequently)

Well, some students need the lectures as a guide to get the basics, before they have enough (insert suitable word) to do the self study and research further

and some topics, such as spectroscopy, one will not understood how they really work without actually measuring a spectrum

there's this hands on experience on building intuition

Anonymous

@SirCumference Things are quite similar here, like most professors teaching very superficially. But it doesn't matter much as I just pay around 7$ for a 6-month semester. XD