Notes for KARCEVSKIJ Sergej Structure of Word

Notes for KARCEVSKIJ Sergej

Structure of Word
TANAKA Akio
September 11, 2011

[Preparation]

<Theorem>

Differential manifold M

M's minimal model of de Rham complex A*(M) M

Isomorphism  exists.

<Definition>

Differential manifold M

When minimal model of M's de Rham complex A*(M) is isomorphic with M's cohomology ring H*(M;R), M is formal.

<Proposition>

What M is formal is equivalent to M has quadrant homology connection.

<Proposition>

Graded differential algebra that satisfies H⁰ (A) = 0 A

Primary minimal model of A exists ρ : M(1) → A

<Interpretation>

Spherical surface is one of formal manifolds.

When manifold is formal, its minimal model is determined by cohomology ring's cup product.

Now word is constructed from minimal model of manifold, that is uniquely determined by cohomology ring's cup product.

This paper has been published by Sekinan Research Field of Language.
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