/sci/ - Science & Math » Thread #11953708

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Anonymous Thu 30 Jul 16:20:03 2020 No.11953708 View Reply Original Report

Quoted By: >>11953751 >>11954051 >>11954348

can a smart person redpill me on k-theory i only know general topology, group theory and what the fundamental group so what is k theory about and what do i need to know to learn about it and in what kind of math is it applied?

Anonymous

Anonymous Thu 30 Jul 2020 16:30:18 No.11953751 Report

Quoted By: >>11953780

>>11953708
>k-theory
some trendy theory 20 years ago. now, nobody gives a shit

k theory, m theory, e theory all cringe and crap

Anonymous

Anonymous Thu 30 Jul 2020 16:38:08 No.11953780 Report

Quoted By:

>>11953751
k theory has nothing to do with m theory

Anonymous

Anonymous Thu 30 Jul 2020 17:55:34 No.11954035 Report

Quoted By: >>11954039 >>11954051

I was never deep into this stuff, but I think K-theory makes a group out of all possible vector bundles and links that group to (co)homological properties, so that you can derive statements either about which vector bundles are possible on a given space or what are the space's topological properties if you have information about its vector bundles.

Anonymous

Anonymous Thu 30 Jul 2020 17:57:41 No.11954039 Report

Quoted By: >>11954051

>>11954035
thanks man but i don't even know what vector bundles are

Anonymous

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Anonymous Thu 30 Jul 2020 18:03:02 No.11954051 Report

Quoted By: >>11954073

>>11953708
I would, but I'm under ethical obligations not to answer stupid shit outside of /sqt/.
[spoiler:lit]I'm also not smart.[/spoiler:lit]
>>11954035
>I think K-theory makes a group out of all possible vector bundles
Yeah. Monoid of vector bundles under direct sum, form a group from it.
For topological K-theory, of course.
>>11954039
You basically continuously associate to every point on a space a vector space.

Anonymous

Anonymous Thu 30 Jul 2020 18:11:27 No.11954073 Report

Quoted By: >>11954101

>>11954051
In this Grothendieck construction you are basically introducing negative dimensional vector bundles. Do you happen to know whether one can associate any physical meaning to those?

Anonymous

Anonymous Thu 30 Jul 2020 18:22:03 No.11954101 Report

Quoted By:

>>11954073
>Do you happen to know whether one can associate any physical meaning to those?
I don't recall any physical interpretations of them.

Anonymous

Anonymous Thu 30 Jul 2020 19:34:38 No.11954348 Report

Quoted By:

>>11953708
It's some boomer field of algebra and geometry. Most K theoriests are at the youngest like 80.

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