Confluence Theory for Graphs
Quantum Algebra
2014-10-01 v1 Geometric Topology
Abstract
We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie algebra of rank at most 2, gives rise to a confluent system of reduction rules of graphs (via Kuperberg's spiders) in an arbitrary surface. As a further consequence of this result, we find canonical bases of SU_3-skein modules of cylinders over orientable surfaces.
Cite
@article{arxiv.math/0609832,
title = {Confluence Theory for Graphs},
author = {Adam S. Sikora and Bruce W. Westbury},
journal= {arXiv preprint arXiv:math/0609832},
year = {2014}
}
Comments
34 pages, 218 figures