The root of language is in the discreteness.Flux Conjecture, Lemma 1 and Lemma 2. 2014-2019 and Note 2020

The root of language is in the discreteness. / All the information of language are generated from this simple structure which supposition is derived from Flux Conjecture, Lemma 1 and Lemma 2. 2014-2019 / With Note 2020

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Root of Language


TANAKA Akio


The root of language is in the discreteness. All the information of language are generated from this simple structure which supposition is derived from Flux Conjecture, Lemma 1 and Lemma 2.


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Floer Homology Language 

TANAKA Akio 

     

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Note 8 

Discreteness of Language​

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Flux Conjecture​

(Lalonde-McDuff-Polterovich 1998)​

Image of Flux homomorphism is discrete at H1(M; R).​

​

Lemma 1​

Next two are equivalent.​

(i) Flux conjecture is correct.​

(ii) All the complete symplectic homeomorphism is C1 topological closed at symplectic 

transformation group.​

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Lemma 2​

Next two are equivalent.​

(1) Flux conjecture is correct.​

(ii) Diagonal set MM×M is stable by the next definition.​

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Definition​

L is stable at the next condition.​

(i) There exist differential 1 form u1, u2 over L that is sufficiently small.​

(ii) When sup|u1|, sup|u2| is Lu1Lu2 for u1, u2 ,there existsf that satisfies u1 - u2  = df .​

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Explanation​

0 ​

​

  is de Rham cohomology class.​

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Symplectic manifold     (M, w)​

Group's connected component of complete homeomorphism       Ham (M, w)​

Flux isomorphism     Flux: π1(Ham(M, w) )→ R​

Road of Ham (M, w)     γ(t)​

δγ / δt = Xu(t) that is defined bu closed differential form Utover M​

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Explanation​

1​

Symplectic manifold     M​

n-dimensional submanifold      L M​

L that satisfies next condition is called special Lagrangian submanifold.​

Ω's restriction to L is L's volume. ​

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2​

M's special Lagrangian submanifold     L​

Flat complex line bundle     L​

LAGsp(M)     (L, L)​

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3​

Complex manifold      M†​

p M†​

Sheaf over M†     fp​

fp (U) = C ( pU)​

fp (U) = 0 ( p U)​

​

4​

Special Lagrangian fiber bundle     π : M → N​

Complementary dimension 2's submanifold     S(N) N​

π-1 (p) = LP​

Pair     (Lp, Lp)​

pN-S(N)​

Lp      Complex flat line bundle​

All the pair (Lp, Lp) s is M0† .​

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5​

(Geometric mirror symmetry conjecture Strominger-Yau-Zaslow 1996)​

Mirror of M is diffeomorphic with compactification of M0† .​

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6 ​

Pairs of Lagrangian submanifold of M and flat U(1) over the submanifold     (L1, L1), (L2, L2)​

(L1, L1)  (L2, L2) means the next.​

There exists complete symplectic homeomorphism that is ψ(L2 ) = L2​

and​

ψ*L2 is isomorphic with L1.​

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Impression​

Discreteness of language is possible by Flux conjecture 1998.​

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[References]​

Quantization of Language / Floer Homology Language / Note 7 / June 24, 2009​

For WITTGENSTEIN Ludwig / Position of Language / Tokyo December 10, 2005​

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To be continued​

Tokyo July 19, 2009​

Sekinan Research Field of Language​

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Back to sekinanlogoshome 

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Source: 
Floer Homology Language / Note 8 / Discreteness of Language / 19 July 2009

Tokyo
20 September 2014
Sekinan Research Field Of Language

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Root of Language Note 
TANAKA Akio 
22 February 2020 SRFL Paper 
Floer Homology Language  Note 8  Discreteness of Language​ shows a root of language. But I think, at least, that the inevitably needed factor must be given at present, when I wrote a paper titled Quantum-Nerve Theory 2019. The must factor is energy, which gives various responses at the presentation of language phenomena. I ever arranged papers related with energy at the next.

Read more: https://srfl-paper.webnode.com/news/the-root-of-language-is-in-the-discreteness-all-the-information-of-language-are-generated-from-this-simple-structure-which-supposition-is-derived-from-flux-conjecture-lemma-1-and-lemma-2-2014-2019-with-note-2020/

Preparation for the energy of language

The energy of language seems to be one of the most fundamental theme for the further step-up  study on language at the present for me. But the theme was hard to put on the mathematical description. Now I present some preparatory  papers written so far.

1. Potential of Language / Floer Homology Language / 16 June 2009
2. Homology structure of Word / Floer Homology Language / Tokyo June 16, 2009
3. Amplitude of meaning minimum / Complex Manifold Deformation Theory / 17 December 2008
4. Time of Word / Complex Manifold Deformation Theory / 23 December 2008

Tokyo

14 May 2019

ENSILA