On spaces of connected graphs I: Properties of Ladders

Details On spaces of connected graphs I: Properties of Ladders On spaces of connected graphs I: Properties of Ladders

2003-01-03

arxiv.org/abs/math/0301018v1

Proc. Internat. Conf. "Knots in Hellas '98", Series on Knots and Everything, vol. 24 (2000), 252-273

Mathematics

Quantum Algebra

16 pages + 6 pages appendix

Scientific paper

We examine spaces of connected tri-/univalent graphs subject to local relations which are motivated by the theory of Vassiliev invariants. It is shown that the behaviour of ladder-like subgraphs is strongly related to the parity of the number of rungs: there are similar relations for ladders of even and odd lengths, respectively. Moreover, we prove that - under certain conditions - an even number of rungs may be transferred from one ladder to another.

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