1992/07/13 by John C. Baez · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #hep-th #math.QA
paper · pdf · doi:10.1007/bf00420517
published as Lett.Math.Phys. 26 (1992) 43-52 · 11 pages
arxiv created 1992/07/13 · openalex publication_date 1992/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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 Vinfinity containing elements gi satisfying the usual braid group relations and elements ai satisfying gi - gi-1 = epsilon ai, where epsilon is a formal variable that may be regarded as measuring the failure of gi2 to equal 1. Topologically, the elements ai 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 Vinfinity. 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.