1 Word is expressed by surface Σ.
2 Word has meaning of starting point, meaning of ending point and time of shift.
3 In surface Σ, oriented closed curve γ and γ’ is presented.
Meaning of starting point is expressed by curve γ.
Meaning of ending point is expressed by curve γ’.
4 In surface Σ, domain D is presented.
Time of shift is expressed by domain D.
5 When γ and γ’make homologous ( γ~γ’ ), their equivalence class gives homology group.
6 In homology group, sequence that consists of Abelian group and homomorphism give boundary operator δ.
When δnoδn+1 = 0 is presented, there gives chain complex.
7 Grammar is expressed by boundary operator.
8 Sentence is expressed by chain complex.
9 When chain group has element z and z makes δz = 0, chain group has cycle group.
10 When chain group has element zp, z and zp+1 makesδzp+1 = z’p , chain group has boundary cycle group.
11 Boundary cycle group is subgroup of cycle group.
12 Boundary cycle group is called phrase.
13 Cycle group is called sentence.
Tokyo May 15, 2007
Sekinan Research Field of Language
www.sekinan.org
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