Monday 24 June 2013

Notes for KARCEVSKIJ Sergej   Condition of Meaning

Condition of Meaning

September 11, 2011

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, ....., xn
Λ (V) = Λ(V)k =Λ (x1, ....., xn )
Operation of minimal model 
Spherical surface Sn, n≥2
de Rham complex *(Sn)
When n iseaven number,
Volume element of S
Mn = Λ (x), |x| = ndx = 0,
M2n-1 gives minimal model Sn to de Rham complex  .
When n is odd number,
Mn gives minimal model Sn to de Rham complex  .
Word is given by spherical surface.
Meaning of word is given by elements x1, ....., xn.
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.

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