Pseudo complex structure on a manifold X of dimension 2N is a C-module structure on a tangent bundle!

[FelixDeCat]

"Pseudo complex structure on a manifold X of dimension 2N is a C-module structure on a tangent bundle."

Can this be explained in laymans terms?

Or maybe a visual perhaps? :shocked:

 

[HamburgerBoy]

Originally posted by: FelixDeKat
Can this be explained in laymans terms?

No, it's impossible.

 

[Saint Nick]

Pseudo means "sort of" or "somewhat".

manifold in math means a surface (or space). X is its label.

2N is the dimensions label.

Tangent, especially during a speech or some other presentation, is some side notes or personal opinions on something. Also can mean something irrelevant to the conversation. Or a "change of course".

A somewhat complex thing in space X of dimension 2N is a C module structure on...

 

[Rogeee]

Sounds like a hipo intake manifold for a rice burner to me.

 

[FelixDeCat]

Originally posted by: jndietz
Pseudo means "sort of" or "somewhat".

manifold in math means a surface (or space). X is its label.

2N is the dimensions label.

Tangent, especially during a speech or some other presentation, is some side notes or personal opinions on something. Also can mean something irrelevant to the conversation. Or a "change of course".

A somewhat complex thing in space X of dimension 2N is a C module structure on...

Your answer seems plausible, but Im curious - if TANGENT is a function on my calculator, does it "digress"?

 

[Eli]

Originally posted by: crustyoldman
Sounds like a hipo intake manifold for a rice burner to me.

:laugh:

 

[Saint Nick]

Originally posted by: FelixDeKat

Originally posted by: jndietz
Pseudo means "sort of" or "somewhat".

manifold in math means a surface (or space). X is its label.

2N is the dimensions label.

Tangent, especially during a speech or some other presentation, is some side notes or personal opinions on something. Also can mean something irrelevant to the conversation. Or a "change of course".

A somewhat complex thing in space X of dimension 2N is a C module structure on...

Your answer seems plausible, but Im curious - if TANGENT is a function on my calculator, does it "digress"?

???

 

[Mo0o]

It means someone set us up the bomb

 

[FelixDeCat]

Tangent, especially during a speech or some other presentation, is some side notes or personal opinions on something. Also can mean something irrelevant to the conversation. Or a "change of course".

I thought a tangent was a mathematical function. Your example pointed to an opinion or side notes related to what is being spoken about or to digress from the main subject.

So I thought a "tangent bundle" was more than just a digression to this declarative statement.

 

[FelixDeCat]

Where are the math geniuses when you need them?

 

[SpecialEd]

The only way I can think of describing this in laymans terms is through an example.

Consider the sphere (a 2 dimensional manifold). At every point you have a tangent plane. The collection of tangent planes is the tangent bundle of the sphere.

The statment says that if I have a complex structure (the points on the sphere behave like complex numbers x+iy), then I get a complex module structure on the tangent bundle (module stucture means there is addition, multiplication and scalar multiplication).

You can do this for other 2 dimension manifolds such as the torus (ie surface of a donut).

 

[SunnyD]

Originally posted by: FelixDeKat
Where are the math geniuses when you need them?

They're all on the TV show NUMB3RS learning leet-speak.

 

[FelixDeCat]

Originally posted by: SpecialEd
The only way I can think of describing this in laymans terms is through an example.

Consider the sphere (a 2 dimensional manifold). At every point you have a tangent plane. The collection of tangent planes is the tangent bundle of the sphere.

The statment says that if I have a complex structure (the points on the sphere behave like complex numbers x+iy), then I get a complex module structure on the tangent bundle (module stucture means there is addition, multiplication and scalar multiplication).

You can do this for other 2 dimension manifolds such as the torus (ie surface of a donut).

My hat is off to you. Thank you. Now the next thing to do is to figure out how to utilize this information in a relatively practical matter.

 

[SpecialEd]

Originally posted by: FelixDeKat

Originally posted by: SpecialEd
The only way I can think of describing this in laymans terms is through an example.

Consider the sphere (a 2 dimensional manifold). At every point you have a tangent plane. The collection of tangent planes is the tangent bundle of the sphere.

The statment says that if I have a complex structure (the points on the sphere behave like complex numbers x+iy), then I get a complex module structure on the tangent bundle (module stucture means there is addition, multiplication and scalar multiplication).

You can do this for other 2 dimension manifolds such as the torus (ie surface of a donut).

My hat is off to you. Thank you. Now the next thing to do is to figure out how to utilize this information in a relatively practical matter.

Thanks

Good luck finding a practical use for it.

 

[quakefiend420]

Originally posted by: Eli

Originally posted by: crustyoldman
Sounds like a hipo intake manifold for a rice burner to me.

:laugh:

WARNING: Danger to manifold!

 

[91TTZ]

It's the secret to the new BitBoys GPU coming out.