Condition of Meaning

Notes for KARCEVSKIJ Sergej

Condition of Meaning
TANAKA Akio
September 11, 2011

[Preparation]

Graded differential algebra 

Minimal model of graded differential algebra 

Degree of homogenious element x of graded differential algabra |x|

Basis of linear space is given by homogenious and elements x₁, ....., x_n

Λ (V) = Λ(V)_k =Λ (x₁, ....., x_n )

Operation of minimal model 

<Example>

Spherical surface Sⁿ, n≥2

de Rham complex *(Sⁿ)

When n iseaven number,

Volume element of S_n 

M_n = Λ (x), |x| = n, dx = 0,

, 

M_2n-1 gives minimal model S_n to de Rham complex  .

When n is odd number,

M_n gives minimal model S_n to de Rham complex  .

[Interpretation]

Word is given by spherical surface.

Meaning of word is given by elements x₁, ....., x_n.

Word has minimal model.

Word becomes formal.

Fundamental group of word contains free group of rank b₁(M).

Here KARCEVSKIJ's "stable part" is identified to fundamental group and " mobile part" is identified to free group.

Refer to the paper Notes for KARVESKIJ Sergej, "Dusualisme asymétrique du signe linguistique" .

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