| Abstract: | We prove necessary and sufficient conditions for an arbitrary invariant of braids with  double points to be the `` derivative' of a braid invariant. We show that the ``primary obstruction to integration' is the only obstruction. This gives a slight generalization of the existence theorem for Vassiliev invariants of braids. We give a direct proof by induction on  which works for invariants with values in any abelian group. We find that to prove our theorem, we must show that every relation among four-term relations satisfies a certain geometric condition. To find the relations among relations we show that  of a variant of Kontsevich's graph complex vanishes. We discuss related open questions for invariants of links and other things. |
