Link invariants of finite type and perturbation theory
- John C. Baez
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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 V x containing elements g i satisfying the usual braid group relations and elements a i satisfying g i−g infi sup-1 =εa i, where ε is a formal variable that may be regarded as measuring the failure of g infi sup2 to equal 1. Topologically, the elements a i 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 V x. We sketch a possible application of link invariants of finite type to a manifestly diffeomorphisminvariant perturbation theory for quantum gravity in the loop representation.
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- Link invariants of finite type and perturbation theory
Letters in Mathematical Physics
Volume 26, Issue 1 , pp 43-51
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- Kluwer Academic Publishers
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- John C. Baez (1)
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- 1. Department of Mathematics, University of California, 92521, Riverside, CA, USA