Symplectic Language Theory Note 2 Gromov-Witten Invariantational Curve

Symplectic Language Theory

TANAKA Akio

   

Note 2

Gromov-Witten Invariantational Curve


[Invariant]
(Gromov-Witten)

[Note]

1 

g, m     Integer that are not less than 0

βH2(M;Z)

Riemann surface of genus g     ∑

Number of element of ∑     m

Group of elements of ∑   

Pseudo regular map     , 

Pair    ((∑, β), φ)

2

All the isomorphism class of ((∑, β), φ)      

Gromov-Witten invariant     Virtual fundamental class of 

[Impression]

1

Language is given by .

2

Word is given by ((∑, β), φ).

3

Word's meaning is given by .

4

Meaning unit is given by pi     (1<i<m)

5

Connection rule of word is given by φ.

[References]

#1 Dirac Operator

#2 TOMONAGA'S Super Multi-time Theory

To be continued

Tokyo February 27, 2009 

References added from NOTE 1 Gromov-Witten Invariant, February 23, 2009 sekinanlogos 

Sekinan Research Field of language

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