Symplectic Language Theory
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 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]
[Map sequence]
Manifold M
Differential 2-form on M w
Symplectic manifold (M, w)
Lagrangian submanifold in (M, w) 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
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