LINK INVARIANTS, HOLONOMY ALGEBRAS, AND FUNCTIONAL-INTEGRATION

Given a principal G-bundle over a smooth manifold M, with G a compact Lie group, and given a finite-dimensional unitary representation rho of G, one may define an algebra of functions on A/G, the ''holonomy Banach algebra'' H-b, by completing an algebra generated by regularized Wilson loops. Elements of the dual H-b* may be regarded as a substitute for measures on A/G. There is a natural linear map from Diff(0)(M)-invariant elements of H-b* to the space of complex-valued ambient isotopy invariants of framed oriented links in M. Moreover, this map is one-to-one when dim M greater than or equal to 3. Similar results hold for a C*-algebraic analog, the ''holonomy C*-algebra.'' (C) 1995 Academic Press, Inc.