nLab
1T relation

Contents

Contents

Idea

In knot theory, by the 1-term relations, or 1T relations for short, one means the relation on the linear span of the set of chord diagrams which relates every chord diagram with an “isolated chord” (one not intersecting any other chord in the diagram) to zero.

The quotient space of the linear span of chord diagrams by the 1T and by the 4T relations is the domain for unframed weight systems on chord diagrams. If one omits the 1T relation and imposes only the 4T relation, one speaks of framed 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


knotsbraids
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

References

Original articles

Textbook accounts

Lecture notes:

Created on November 26, 2019 at 07:18:07. See the history of this page for a list of all contributions to it.