Description of Language

<Preparation>

Manifold M

Cup product map of M

Dual map of

Free Lie algebra that generates £ ( )

is identified as the partial space of £( ) that quadrastic Lie bracket of 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 .

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

<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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