Floer Homology Language
Note5
Homology Generation of Language
1
Isomorphism class of manifold moduli space
Moduli space M
2
Compactification of Mg, k CMg, k
3
Compact Hausdorff space Σ
Riemann surface that has finite sum that is not intersected each other
Continuous map π : →Σ
There exists finite set S(Σ)
Σ.
π's restriction
is homeomorphism.
consists of 2 points over 
Structure over Σ is abbreviatedly called semistable curve.
4
z1, ..., zk is different regular point. （Σ、
) is called k pointed semistable curve.
3
Pointed semistable curve （Σ、) is stable. Automorphism Aut（Σ、) group is finite group.
5
Simply-connected and connected compact 1-dimensional simplicial complex tree
Stable curve that has genus 0 Σ
Tree ΓΣ
6
Tree Γ
Vertex number that each vertex has only one side k+1
Tree that has k+1 vertexes TRk+1
Γ
TRk+1
Stable curve Σ that is ΓΣ = Γ CM (Γ)
7
(Theorem, Knudsen-Keel)
Homology group
is generated from fundamental group of CM (Γ).
8
ΓTRm+1
shh : RT k+1 →TRm+1
h0 : {1, 2, 3, 4} →{1, ..., k}
shh0 is expressed by sh.
9
Forgetting map fg : Mg,k (M,JM;β) →Mg,k
10
There exists next equality at.
(1)
11
(Theorem, Knudsen-Keel)
is generated by 
.
is vector space expressed by relation (1).
[Image]
It is seemed to be existential that language is expressed by homology.
[References]
1
Isomorphism class of manifold moduli space
Moduli space M
2
Compactification of Mg, k CMg, k
3
Compact Hausdorff space Σ
Riemann surface that has finite sum that is not intersected each other
Continuous map π :
→ΣThere exists finite set S(Σ)
Σ.π's restriction
is homeomorphism. consists of 2 points over Structure over Σ is abbreviatedly called semistable curve.
4
z1, ..., zk is different regular point. （Σ、
) is called k pointed semistable curve.3
Pointed semistable curve （Σ、
) is stable. Automorphism Aut（Σ、) group is finite group. 5
Simply-connected and connected compact 1-dimensional simplicial complex tree
Stable curve that has genus 0 Σ
Tree ΓΣ
6
Tree Γ
Vertex number that each vertex has only one side k+1
Tree that has k+1 vertexes TRk+1
Γ
TRk+1Stable curve Σ that is ΓΣ = Γ CM (Γ)
7
(Theorem, Knudsen-Keel)
Homology group
is generated from fundamental group of CM (Γ).8
Γ
TRm+1shh : RT k+1 →TRm+1
h0 : {1, 2, 3, 4} →{1, ..., k}
shh0 is expressed by sh.
9
Forgetting map fg : Mg,k (M,JM;β) →Mg,k
10
There exists next equality at
. (1)11
(Theorem, Knudsen-Keel)
is generated by . is vector space expressed by relation (1).[Image]
It is seemed to be existential that language is expressed by homology.
[References]
On Time Property Inherent in Characters / Hakuba March 28, 2003
Prague Theory 3 / Tokyo January 28, 2005
Generation Theorem / von Neumann Algebra 2 / Note / Tokyo April 20, 2008
Homological Mirror Symmetry Conjecture by KONTSEVICH / Symplectic Language Theory / Note 6 / Tokyo April 26, 2009
Prague Theory 3 / Tokyo January 28, 2005
Generation Theorem / von Neumann Algebra 2 / Note / Tokyo April 20, 2008
Homological Mirror Symmetry Conjecture by KONTSEVICH / Symplectic Language Theory / Note 6 / Tokyo April 26, 2009
Tokyo June 11, 2009
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