/sci/ - Science & Math

[Anonymous No.11503670]

What is a result that you find fascinating that you are studying in this period? For me it's the Van Kampen theorem

[Anonymous No.11503859]

>>11503670
I recall that there's a proof of the fact that subgroups of free groups are free, using the Van Kampen theorem. It's extremely aryan desu

[Anonymous No.11503890]

>>11503670
>pi_1 takes pushouts to pushouts
Deep

>>11503859
Yes, it's trivial because wedge sums of circles have free fundamental groups.

[Anonymous No.11503904]

>>11503890
>pi_1 takes pushouts to pushouts
It doesn't in general, only when the pushout diagram is formed by nice inclusions. If you're gonna be a fag, at least do it right.

[Anonymous No.11503945]

>>11503890
>Yes, it's trivial because wedge sums of circles have free fundamental groups.
And how does that imply that a subgroup of a free group is free?

[Anonymous No.11503955]

>>11503945
Nevermind, looked it up.

[Anonymous No.11503959]

>>11503904
I never said what category I was working in. Who's the fag now?

[Anonymous No.11503963]

>>11503670
How can anybody be interested in this dry shit?

[Anonymous No.11504644]

>>11503963
what do you find non dry shit ?

[Anonymous No.11505686]

>>11503963
ur dry shit

[Anonymous No.11505736]

>>11504644
DA NUMBA THEOREZ

[Anonymous No.11505805]

I like wheels but that's just me
https://en.wikipedia.org/wiki/Wheel_theory
Anton Setzer - Wheels
http://www.cs.swan.ac.uk/~csetzer/articles/wheel.pdf
Jesper Carlstrom - Wheels: On Division by Zero
http://www2.math.su.se/reports/2001/11/2001-11.pdf
keep on rollin'

[Anonymous No.11505811]

>>11505805
Why do you like them? Aren't they useless garbage? A curiosity for kindergarten kids.

[Anonymous No.11505941]

>>11505811
Well, it sounds like someone knows less about wheel theory than wheel theory knows about him! Here's a little tip, kid: you can never hope to defeat your enemies without knowing how they think. And by the time you know enough wheel theory to fight the wheel theoretic, it's already too late. You're already a wheel theorist.

[Anonymous No.11505947]

>>11505941
Your inability to come up with any reasons why it's interesting affirms my suspicion that it's useless garbage.

[Anonymous No.11505967]

>>11503670
I want to get to this point in math where I can hopefully understand this shit.

[Anonymous No.11505978]

>>11505947
Why are ye fearful, O ye of little faith?

[Anonymous No.11506069]

>>11505967
read Lee's topological manifolds

[Anonymous No.11507045]

>>11505805
Wheel theory? Is that like.. actual fucking wheels that spin and shit, or is this another "ring-theory" thing where the name is misleading?
>>11505811
>Aren't they useless garbage? A curiosity for kindergarten kids.
I've said this kind of thing at different times in my math career yet I was almost always making hasty remarks about the significance of those subjects. This considered, I will stake a coin toss to decide wheel theory is the real deal.
>>11505941
>Well, it sounds like someone knows less about wheel theory than wheel theory knows about him! Here's a little tip, kid: you can never hope to defeat your enemies without knowing how they think. And by the time you know enough wheel theory to fight the wheel theoretic, it's already too late. You're already a wheel theorist.
So many fucking red flags. I'm raising the stakes, now it's like 1/10 chance that Wheel theory is fucking awesome, 9/10 it's a meme. Fuck it, I'm going in.
>https://en.wikipedia.org/wiki/Wheel_theory
>http://www.cs.swan.ac.uk/~csetzer/articles/wheel.pdf
>http://www2.math.su.se/reports/2001/11/2001-11.pdf
Bravo, Anon. That was stupider than I thought it was going to be.

[Anonymous No.11508319]

>>11507045
premium /sci/

[Anonymous No.11509291]

>>11507045
ring is not for circle, but - akin to "group", "set" or "category" - denotes a collection of thing. Think crime ring.

[Anonymous No.11509316]

>>11503670
The proof that the whitehead square of the identity spheroid S^2n -> S^2n has infinite order in pi_(4n-1)(S^(2n)) using the Hopf invariant is extremely cool!

[Anonymous No.11510351]

>>11505941
based wheel theorist

[Anonymous No.11510385]

>>11503670

Diagrams very similar to this one were used in the algebraic work of Steven Haataja (et al), who died under gruesome and mysterious circumstances in Chadon, Nebraska. He was found tied to a tree and burned to death.

https://arxiv.org/pdf/1007.1192.pdf

There's this joint paper and his dissertation which is on similar subject matter (which I think also contains a similar diagram but I'm not sure).

[Anonymous No.11510405]

>>11510385
>vixra

[Anonymous No.11510543]

>>11510405

Not the point.

[Anonymous No.11510960]

>>11507045
There are wheels within wheels in this village, and fires within fires!

[Anonymous No.11511366]

A theorem of Martin and Harrington linking determinancy to large cardinals.
[math]\Sigma_1^1(x)[/math]-determinancy if and only if [math]x^{\sharp}[/math] exists for every [math]x\subseteq\omega[/math]. In particular, if there exists a measurable cardinal then [math]\mathbf{\Sigma}_1^1[/math]-determinancy holds, since a measureable cardinal implies the existence of sharps and [math]\displaystyle\mathbf{\Sigma}_1^1=\bigcup_{x\in \omega^{\omega}}\Sigma_1^1(x)[/math]. This result is sharp since Borel determinacy holds in [math]\mathtt{ZFC}[/math].