Examples/classes:
Types
Related concepts:
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 diagrams | weight systems |
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linear chord diagrams, round chord diagrams Jacobi diagrams, Sullivan chord diagrams | Lie algebra weight systems, stringy weight system, Rozansky-Witten weight systems |
Original articles
Dror Bar-Natan, On the Vassiliev knot invariants, Topology Volume 34, Issue 2, April 1995, Pages 423-472 (doi:10.1016/0040-9383(95)93237-2, pdf)
Dror Bar-Natan, Vassiliev and Quantum Invariants of Braids, Geom. Topol. Monogr. 4 (2002) 143-160 (arxiv:q-alg/9607001)
Textbook accounts
Sergei Chmutov, Sergei Duzhin, Jacob Mostovoy, Section 4 of: Introduction to Vassiliev knot invariants, Cambridge University Press, 2012 (arxiv/1103.5628, doi:10.1017/CBO9781139107846)
David Jackson, Iain Moffat, Section 11 of: An Introduction to Quantum and Vassiliev Knot Invariants, Springer 2019 (doi:10.1007/978-3-030-05213-3)
Lecture notes:
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