Notes for AKT-090917-1/0:20:08: Difference between revisions

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Def: 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</math>-singular knots)
''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).

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.
''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.

We can also express the 'type <math>m</math>' condition as:
:<math>V(\doublepoint ... \doublepoint)=0</math>

whenever we have more than <math>m</math> double points.

Latest revision as of 20:28, 4 September 2011

Definition: A knot invariant is of Vassiliev type if (on the whole space of -singular knots).

Notation: We drop the superscript in since for each , is only defined for -singular knots.

We can also express the 'type ' condition as:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V(\doublepoint ... \doublepoint)=0}

whenever we have more than double points.

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