Isomorphism of Map Sequence

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Symplectic Language Theory

TANAKA Akio

   

Note4

Isomorphism of Map Sequence


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

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

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


[References]

<Early papers on the theme>

#1 Guarantee of Language

#2 Mirror Language

#3 Actual Language and Imaginary Language

<Symplectic Language Theory>

#4 Symplectic Language Theory / Note 3 / Mirror Symmetry Conjecture on Rational Curve

^{_{To be continued}}

^{_{Tokyo March 9, 2009}}

^{_{Sekinan Research Field of language}}

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