A four-term relation, also called a 4T relation, is a linear equation relating four chord diagrams obtained
by moving one endpoint of a chord past either endpoint
of another chord. Fix a chord
with endpoints 
and 
,
and another chord with one endpoint fixed at 
. Write 
and 
for the diagrams in which its other endpoint lies immediately
before and after 
,
respectively, in the manifold orientation
of the circle. Define 
and 
similarly at 
. The endpoints 
, 
and 
are distinct, and the small neighborhoods
in which the moving endpoint is placed contain no other endpoints. All other endpoints
and pairings remain fixed. The relation is
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Imposing all such relations on the vector space generated by chord diagrams gives the algebra of chord diagrams (Bar-Natan 1995).
