sekinanlogoshome
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
Source: https://writer.zoho.com/public/sekinan/TGLT2FromFinitenessToInfinityOnLanguage
Source: https://writer.zoho.com/public/sekinan/TGLT2FromFinitenessToInfinityOnLanguage
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