On spaces of connected graphs II: Relations in the algebra Lambda
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 Lambda0 that is generated by certain elements called t and xn with n >= 3. Two families of relations in Lambda0 are derived and it is shown that the dimension of Lambda0 grows at most quadratically with respect to degree. Under the assumption that t is not a zero divisor in Lambda0, a basis of Lambda0 and an isomorphism from Lambda0 to a sub-ring of Z[t,u,v] is given.
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