Topological Group Language Theory Preliminary Note 2 From Finiteness to Infinity on Language

Topological Group Language Theory

TANAKA Akio

   

Preliminary Note 2

From Finiteness to Infinity on Language


[Theorem]
(Bestvina-Feighn)
G is finite representation group and is not almost abelian group.
Hn is n-dimensional hyperbolic space.
Isometric transformation group that has orientation in Hn    Isom+(Hn)
G's all the faithful and discrete representation to  Isom+(Hn)     HomFD(G,  Isom+(Hn))
Space that is divided by conjugation by the element of  Isom+(Hn)     HomFD(G,  Isom+(Hn)) / conj.
For a certain n, HomFD(G,  Isom+(Hn)) / conj. is not compact.
G is decomposed on subgroup that is almost abelian group.

[Impression]
Process from word to Language is analogous to the situation of almost abelian group in subgroup to not-abelian group in G.
Recognition of language is also analogous with abelian and not-abelian group in G against finiteness of word and infinity on sentence or language.


[References]
<On recognition>
#1 Recognition
#2 Understandability of Language
<On word>
#3 From Cell to Manifold
#4 Geometry of Word
<On grammar>
#5 Grammar
<On language>
#6 Orbit of Word

To be continued

Tokyo February 1, 2009

Sekinan Research Field of language