On spaces of connected graphs II: Relations in the algebra Lambda
Quantum Algebra
2007-05-23 v1 Geometric Topology
Abstract
The graded algebra Lambda defined by Pierre Vogel is of general interest in the theory of finite-type invariants of knots and of 3-manifolds because it acts on the corresponding spaces of connected graphs subject to relations called IHX and AS. We examine a subalgebra Lambda_0 that is generated by certain elements called t and x_n with n >= 3. Two families of relations in Lambda_0 are derived and it is shown that the dimension of Lambda_0 grows at most quadratically with respect to degree. Under the assumption that t is not a zero divisor in Lambda_0, a basis of Lambda_0 and an isomorphism from Lambda_0 to a sub-ring of Z[t,u,v] is given.
Cite
@article{arxiv.math/0301019,
title = {On spaces of connected graphs II: Relations in the algebra Lambda},
author = {Jan Kneissler},
journal= {arXiv preprint arXiv:math/0301019},
year = {2007}
}
Comments
8 pages