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
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
Root of Language / 20 September 2014
May 23, 2019
Root of Language / 20 September 2014
20/09/2014 10:02 Root of LanguageTANAKA AkioThe 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 LanguageTANAKA Akio
Note 8
Discreteness of Language
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.
Lemma 2
Next two are equivalent.
(1) Flux conjecture is correct.
(ii) Diagonal set M
M×M is stable by the next definition. 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 . Explanation 0 is de Rham cohomology class. 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 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. 2 M's special Lagrangian submanifold L Flat complex line bundle L LAGsp(M) (L, L) 3 Complex manifold M† p M† Sheaf over M† fp fp (U) = C ( pU) fp (U) = 0 ( pU) 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† . 5 (Geometric mirror symmetry conjecture Strominger-Yau-Zaslow 1996) Mirror of M is diffeomorphic with compactification of M0† . 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. Impression Discreteness of language is possible by Flux conjecture 1998. [References] Quantization of Language / Floer Homology Language / Note 7 / June 24, 2009 For WITTGENSTEIN Ludwig / Position of Language / Tokyo December 10, 2005 To be continued Tokyo July 19, 2009 Sekinan Research Field of Language Back to sekinanlogoshome ................................................................................................................ Source: Floer Homology Language / Note 8 / Discreteness of Language / 19 July 2009Tokyo20 September 2014Sekinan Research Field Of Language Read more: https://srflnote.webnode.com/news/root-of-language-20-september-2014/
Root of Language NoteTANAKA Akio22 February 2020SRFL PaperFloer Homology LanguageNote 8 Discreteness of Languageshows 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.
M×M is stable by the next definition. 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 Lu1
Lu2 for u1, u2 ,there existsf that satisfies u1 - u2 = df . Explanation 0 
is de Rham cohomology class. 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 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. 2 M's special Lagrangian submanifold L Flat complex line bundle L LAGsp(M) (L, L) 3 Complex manifold M† p 
M† Sheaf over M† fp fp (U) = C ( p
U) 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) p
N-S(N) Lp Complex flat line bundle All the pair (Lp, Lp) s is M0† . 5 (Geometric mirror symmetry conjecture Strominger-Yau-Zaslow 1996) Mirror of M is diffeomorphic with compactification of M0† . 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. Impression Discreteness of language is possible by Flux conjecture 1998. [References] Quantization of Language / Floer Homology Language / Note 7 / June 24, 2009 For WITTGENSTEIN Ludwig / Position of Language / Tokyo December 10, 2005 To be continued Tokyo July 19, 2009 Sekinan Research Field of Language Back to sekinanlogoshome ................................................................................................................ Source: Floer Homology Language / Note 8 / Discreteness of Language / 19 July 2009 Tokyo 20 September 2014 Sekinan Research Field Of Language Read more: https://srflnote.webnode.com/news/root-of-language-20-september-2014/
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