nLab 2T relation




In knot theory the 2-term relations on horizontal chord diagrams are the following relations in the linear span of the set of horizontal chord diagrams:

For pairwise distinct indices i,j,k,li,j,k,l, the (i,j)(i,j)-chord generator commutes with the (k,l)(k,l)-chord generator, for instance:

graphics from Sati-Schreiber 19c

Together with the horizontal 4T relations these are the relations respected by horizontal weight systems.

chord diagramsweight systems
linear chord diagrams,
round chord diagrams
Jacobi diagrams,
Sullivan chord diagrams
Lie algebra weight systems,
stringy weight system,
Rozansky-Witten weight systems

chord diagram,
Jacobi diagram
horizontal chord diagram
1T&4T relation2T&4T relation/
infinitesimal braid relations
weight systemhorizontal weight system
Vassiliev knot invariantVassiliev braid invariant
weight systems are associated graded of Vassiliev invariantshorizontal weight systems are cohomology of loop space of configuration space


Last revised on September 9, 2023 at 08:09:40. See the history of this page for a list of all contributions to it.