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/sci/ - Science & Math

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10164558 No.10164558 [Reply] [Original]

Dear theoretical phy/sci/ists.
In this thread we'll talk about Calabi-Yau Manifolds.

If you don't know much, here are two easy-to-read introductions to the topic: https://ncatlab.org/nlab/show/Calabi-Yau+variety
http://www.scholarpedia.org/article/Calabi-Yau_manifold

>> No.10164571

>>10164558
Applications?

>> No.10164602

>>10164558
sauce? I remember seeing some touhou manga edited with topology text as well, would appreciate if some anons could help me find it as wel..

>> No.10164645

>>10164602
looks like Kotomi Ichinose from Clannad but I could be wrong

>> No.10164710
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10164710

>>10164558
>http://www.scholarpedia.org/article/Calabi-Yau_manifold

Weeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee~

>> No.10164722

6-D continuous manifolds, so?

>> No.10164728

>>10164722
>6d

My disgust is in the 6th dimension.

>> No.10164808

>>10164722
Retard.

>> No.10164818
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10164818

I guess Kaluza-Klein theory happens in a CY manifold with O(4) x SU(1) homology.
>Kaluza-Klein Gravity
>https://arxiv.org/abs/gr-qc/9805018

My own theory can't live in a CY manifold because I have two separate KK spaces, each a CY manifold. However, I think the extension of the homology to include a dual is no huge hurdle

>> No.10164825

>>10164818
That's one interpretation.

People don't seem to understand the liquidity of their own creations.

>> No.10164833 [DELETED] 

>>10164818
>I guess Kaluza-Klein theory happens in a CY manifold with O(4) x SU(1) homology.


So many things wrong with this statement. The Kaluza-Klein mechanism is a general framework for dimensional compactification, it is not compactification is just a special case.

SU(1) is a trivial group

Homology groups are abelian, O(4) is not.

>> No.10164834

>>10164818

So many things wrong with this statement. The Kaluza-Klein mechanism is a general framework for dimensional compactification, CY-compactification is just a special case.

SU(1) is a trivial group

Homology groups are abelian, O(4) is not.

>> No.10164899
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10164899

>>10164602

>> No.10164904

The words... They're not human shaped

>> No.10165838

>>10164645
She does look like Kotomi

>> No.10165885

>>10164722
>continuous manifolds
That is a tautology.

>> No.10166721

>>10165885
How is that a tautology? Isn't a manifold just locally homeomorphic to an euclidean space?
For example: not just a sphere but also a cube

>> No.10166923

>>10164899
I broke it.

>> No.10167258

>>10166721
is [0,1] a 1-manifold?

>> No.10167282

>>10166721
All manifolds are continuous.
>>10164722
They're very special 6D manifolds.

>> No.10167286

>>10164818
>a CY manifold with O(4) x SU(1) homology
You have no idea what homology is.
>>10167258
It's a manifold with boundary.

>> No.10167289
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10167289

>>10164558
>doesn't invite complex geometers

>> No.10168003 [DELETED] 

>>10166721
A sphere is still continuous. You are thinking smoothness.

>> No.10168032

>>10166721
A cube is still continuous. You are thinking smoothness.

>> No.10169916

>>10164558
bump

>> No.10170898

>>10164558
bump

>> No.10171173

>>10167258
No, it's a set of real non-negative numbers. If you provide me with a topology and an atlas of charts covering the space, then yes you have a (topological) manifold. You'll notice that this actually isn't possible under the standard topology because of the endpoints making it impossible to use open covers to cover the entire space. Fortunately, there is a notion of manifold with boundary, which requires us to slightly modify our definition of a chart, but in fact every manifold is a manifold with boundary (the converse is obviously not true, per this example), so it is a reasonable definition to make.
tl;dr [0, 1] with the appropriate structute can be a (topological) manifold with boundary.

>> No.10171630

I'm currently studying Kähler cones of compact 6d Kähler, more specifically 6d CY manifolds. Apparently the topology of the Kähler cone in the positive (or index) cone is a delicate matter. Any suggestion on this topic would be very much appreciated

>> No.10171708

>>10171173
>what you are referring to as interval is actually interval/topology, or as i've recently taken to calling it, interval+topology

>> No.10172985

>>10164558
bump

>> No.10174502

>>10171708
Or you know a subspace topology of the topology on the extended real line?

>> No.10174617

Anyone here study BPS states/refined Donaldson Thomas invariants on 3-CYs?
Working on D4 singularities here.