2015
Connection matrices and Lie algebra weight systems for multiloop chord diagrams
Publication
Publication
Journal of Algebraic Combinatorics , Volume 42 - Issue 4 p. 893- 905
We give necessary and sufficient conditions for a weight system on multi-
loop chord diagrams to be obtainable from a metrized Lie algebra representation, in
terms of a bound on the ranks of associated connection matrices. Here a multiloop
chord diagram is a graph with directed and undirected edges so that at each vertex,
precisely one directed edge is entering and precisely one directed edge is leaving,
and each vertex is incident with precisely one undirected edge. Weight systems on
multiloop chord diagrams yield the Vassiliev invariants for knots and links. The
k-th connection matrix of a function f on the collection of multiloop chord diagrams is
the matrix with rows and columns indexed by k-labeled chord tangles and with entries
equal to the f value on the join of the tangles.
Additional Metadata | |
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Springer | |
Journal of Algebraic Combinatorics | |
Networks | |
Organisation | Networks and Optimization |
Schrijver, L. (2015). Connection matrices and Lie algebra weight systems for multiloop chord diagrams. Journal of Algebraic Combinatorics, 42(4), 893–905. |