Perspective 2 Symplectic Approach

sekinanlogoshome

Perspective 2

TANAKA Akio

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.
PointpM
Neighborhood     U_p    
Differential homeomorphism     φ : U_p→ Cⁿ
φ*w₀ = w
w₀ = Σdx_idy_i
(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}

_{Sekinan Research Field of language}

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