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

Latest revision as of 20:28, 4 September 2011

Definition: A knot invariant $V$ is of Vassiliev type $m$ if $V^{(m+1)}=0$ (on the whole space of $(m+1)$ -singular knots).

Notation: We drop the superscript in $V^{(m)}$ since for each $m$ , $V^{(m)}$ is only defined for $m$ -singular knots.

We can also express the 'type $m$ ' condition as:

Failed to parse (unknown function "\doublepoint"): {\displaystyle V(\doublepoint ... \doublepoint)=0}

whenever we have more than $m$ double points.

@@ Line 1: / Line 1: @@
-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.