  The Vassiliev-Gusarov link invariants of finite type are known to be closely
related to perturbation theory for Chern-Simons theory. In order to clarify the
perturbative nature of such link invariants, we introduce an algebra V_infinity
containing elements g_i satisfying the usual braid group relations and elements
a_i satisfying g_i - g_i^{-1} = epsilon a_i, where epsilon is a formal variable
that may be regarded as measuring the failure of g_i^2 to equal 1.
Topologically, the elements a_i signify crossings. We show that a large class
of link invariants of finite type are in one-to-one correspondence with
homogeneous Markov traces on V_infinity. We sketch a possible application of
link invariants of finite type to a manifestly diffeomorphism-invariant
perturbation theory for quantum gravity in the loop representation.
