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.
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