Noncommutative Distance Theory
Note 5
Kontsevich Invariant
TANAKA Akio
R3 : = C × R
Knot K
Parameter of height t
Two points on K at t z ( t ) z’ ( t )
Selected point of z and z’ P
z and z’ Code figure on S1 DP
Iteration integral Z’ ( K ) : =
Σm=0∞
×
(-1)#P1DP![](file:///C:/Users/master/Documents/My%20Web%20Sites/SRFL/SekinanLinguisticField/NDTNote5KontsevichInvariant.files/image008.gif)
![](file:///C:/Users/master/Documents/My%20Web%20Sites/SRFL/SekinanLinguisticField/NDTNote5KontsevichInvariant.files/image002.gif)
![](file:///C:/Users/master/Documents/My%20Web%20Sites/SRFL/SekinanLinguisticField/NDTNote5KontsevichInvariant.files/image004.gif)
![](file:///C:/Users/master/Documents/My%20Web%20Sites/SRFL/SekinanLinguisticField/NDTNote5KontsevichInvariant.files/image006.gif)
![](file:///C:/Users/master/Documents/My%20Web%20Sites/SRFL/SekinanLinguisticField/NDTNote5KontsevichInvariant.files/image008.gif)
Quotient vector space that is quoted by 3 relations ( AS, IHX and STU )* over C on which Jacobi figure is described A ( S1 )
Kontsevich invariant Z ( K ) ∈ A ( S1 )
[Note]
*3 relations ( AS, IHX and STU ) are seemed to be related with characters’ descriptive system.
Tokyo January 3, 2008
Sekinan Research Field of Language
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