Thursday 2 December 2021

Floer Homology Language Note 7 Quantization of Language​

 

Floer Homology Language Note 7 Quantization of Language​

Floer Homology Language 
    
 
Note 7 
 
Quantization of Language
Theorem
1
(Barannikov, Kontsevich 1998)
<.,.>, ° defines structure of Frobenius manifold at neighborhood of H's origin.
2
(Kontsevich 2003)
There exists φk : EkΠ2(Γ(M;Ω(M))) → Π2CD(AA), k = 2, ... .
 is L map.
Explanation
1
(Local coordinates of Poisson structure)
{f, g} 
2
(Map)
{.,.} : C × C  →C
The map  has next conditions.
(i)   {.,.} is R bilinear,{f, g} = - {g, f}.
(ii)  Jacobi law is satisfied.
(iii) {fgh} = g{f, h} + h{f, g}
3
(Gerstenharber bracket)
4
5
6
7
8
 )
Manifold     MR2n
Coordinates     p, q
Differential form     w = dqidpi
Subset of C( R2n )        A
Element of A       F    
Differential operator of R2n      D(F)
D({FG}) ≡ [D({F}, D({G}]
[Image 1]
Quantization of language is defined by theorem (Kontsevich 2003).
[Image 2]
Complex unit  is seemed to be essential for mirror symmetry of language by explanation 
8.
[References] 


Read more: https://srfl-lab.webnode.com/products/floer-homology-language-note-7-quantization-of-language/

No comments:

Post a Comment