Link invariants of finite type and perturbation theory
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- Baez, J.C. Lett Math Phys (1992) 26: 43. doi:10.1007/BF00420517
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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 Vx containing elements gi satisfying the usual braid group relations and elements ai satisfying gi−ginfisup-1=εai, where ε is a formal variable that may be regarded as measuring the failure of ginfisup2to equal 1. Topologically, the elements ai signify intersections. We show that a large class of link invariants of finite type are in one-to-one correspondence with homogeneous Markov traces on Vx. We sketch a possible application of link invariants of finite type to a manifestly diffeomorphisminvariant perturbation theory for quantum gravity in the loop representation.