On spaces of connected graphs II: Relations in the algebra Lambda

摘要

The graded algebra Lambda defined by Pierre Vogel is of general interest inthe theory of finite-type invariants of knots and of 3-manifolds because itacts on the corresponding spaces of connected graphs subject to relationscalled IHX and AS. We examine a subalgebra Lambda_0 that is generated bycertain elements called t and x_n with n >= 3. Two families of relations inLambda_0 are derived and it is shown that the dimension of Lambda_0 grows atmost quadratically with respect to degree. Under the assumption that t is not azero divisor in Lambda_0, a basis of Lambda_0 and an isomorphism from Lambda_0to a sub-ring of Z[t,u,v] is given.