Perspective
Perspective 1
Symplectic Approach
1
Language universal is regarded as a type of invariant.
2
Gromov-Witten invariant is only determined by symplectic manifold.
3
Gromov-Witten invariant is invariant by continuous deformation of symplectic structure.
4
Gromov-Witten invariant is regarded as a language universal.
5
Language consists of words.
6
Word model is given by symplectic manifold.
Manifold M
2 differential form w
dw = 0
wn ≠ 0
Symplectic manifold (M, w)
7
(Darboux)
Word consist of a point, its neighborhood and differential homeomorphim that is from the
neighborhood to Cn.
Pointp
M
Neighborhood Up
Differential homeomorphism φ : Up→ Cn
φ*w0 = w
w0 = Σdxi
dyi
(Complex coordinate zi = xi +
yi )
8
Word model is also given by spherical object.
9
Sentence model is given by exact sequence of chain complex.
[References]
Basic papers for the themes are seen at
Sekinan Linguistic Field.
Recent papers are seen at
sekinanlogos.
To be continued
Tokyo February 19, 2009
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