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Root of Language / 20 September 2014 May 23, 2019 Root of Language / 20 September 2014 20/09/2014 10:02 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. ......................................................................................................................................... Floer Homology Language TANAKA 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 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/
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.
Preparation for the energy of language May 14, 2019 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. Potential of Language / Floer Homology Language / Potential of Language / 16 June 2009 Homology structure of Word / Floer Homology Language /Homology Structure of Word / Tokyo June 16, 2009 Amplitude of meaning minimum / Complex Manifold Deformation Theory / 17 December 2008 Time of Word / Complex Manifold Deformation Theory / 23 December 2008 Tokyo 14 May 2019 ENSILA
22 February 2020 SRFL Paper