Wednesday 27 March 2013

Symplectic Language Theory Note4 Isomorphism of Map Sequence


Symplectic Language Theory

   
Note4
Isomorphism of Map Sequence


[Map sequence]
Manifold     M
Differential 2-form on M      w
Symplectic manifold     (Mw)
Lagrangian submanifold in  (Mw)      L
Isotopy class of L    Liso   
All the equivalece class by lagrangian submanifold's Hamiltonian homeomorphism of Liso     Ms(M, Liso)
3-dimensional Calabi-Yau manifold     M#
Moduli space of M#'s complex structure     Mc(M#)
Complex vector bundle     E --> M# 
Pair     Mc(M#, E)
Map sequence of Mc     Mc(E) --> Mc(M#, E) --> Mc(M#           (1)
Map sequence of Ms    Ms (Liso) --> Ms (M, Liso) --> Ms (M)        (2)

[Conjecture]
When  (M#, E) is mirror for (M, Liso), map sequence (1) and (2) become isomorphism. 

[Impression]
1
 When(M#, E) is given to be word(M,Liso)is given to be mirror word.
2
E is given to be meaning minimum of word.
3
Liso is given to be mirror meaning whole that is base of mirror word.


[References]
<Early papers on the theme>

To be continued
Tokyo March 9, 2009


No comments:

Post a Comment