Notes for AKT-090917-1/0:20:08: Difference between revisions
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''Definition'': A knot invariant <math>V</math> is of '''Vassiliev type <math>m</math>''' if <math>V^{(m+1)} = 0</math> (on the whole space of <math>(m+1)</math>-singular knots). |
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Notation: |
''Notation'': We drop the superscript in <math>V^{(m)}</math> since for each <math>m</math>, <math>V^{(m)}</math> is only defined for <math>m</math>-singular knots. |
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We can also express the 'type <math>m</math>' condition as: |
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:<math>V(\doublepoint ... \doublepoint)=0</math> |
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whenever we have more than <math>m</math> double points. |
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Latest revision as of 20:28, 4 September 2011
Definition: A knot invariant [math]\displaystyle{ V }[/math] is of Vassiliev type [math]\displaystyle{ m }[/math] if [math]\displaystyle{ V^{(m+1)} = 0 }[/math] (on the whole space of [math]\displaystyle{ (m+1) }[/math]-singular knots).
Notation: We drop the superscript in [math]\displaystyle{ V^{(m)} }[/math] since for each [math]\displaystyle{ m }[/math], [math]\displaystyle{ V^{(m)} }[/math] is only defined for [math]\displaystyle{ m }[/math]-singular knots.
We can also express the 'type [math]\displaystyle{ m }[/math]' condition as:
- [math]\displaystyle{ V(\doublepoint ... \doublepoint)=0 }[/math]
whenever we have more than [math]\displaystyle{ m }[/math] double points.
