Description of Language
TANAKA Akio
September 9, 2011
<Preparation>
Manifold M
Cup product map of M 

Dual map of



Free Lie algebra that
generates £ (
)





Ideal of £(
) that Im η generates a

Holonomy Lie algebra of M 

Completion of holonomy Lie algebra 

<Theorem>
If M has quadrastic homology connection, Malcev completion
becomes isomorphic with holonoly Lie algebra completion
.
If M has quadrastic homology connection, Malcev completion


<Therorem>
Primary minimum model M(1)of differential manifold M is isomorphic with Malcev completion of
of M's fundamental group.
Primary minimum model M(1)of differential manifold M is isomorphic with Malcev completion of

<Inrterpretation>
For the description of a language model there is a need primary minimum model M(1) of differential manifold M.
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