QUANTUM THEORY OF NON-ABELIAN DIFFERENTIAL FORMS AND LINK POLYNOMIALS

A topological quantum field theory of non-Abelian differential forms is investigated from the point of view of its possible applications to description of polynomial invariants of higher-dimensional two-component links. A path-integral representation of the partition function of the theory, which is a highly on-shell reducible system, is obtained in the framework of the antibracket-antifield formalism of Batalin and Vilkovisky. The quasi-monodromy matrix, giving rise to corresponding skein relations, is formally derived in a manifestly covariant non-perturbative manner.

On the generalized Teichmüller spaces and differential equations

It is well known that for the family F of Riemann surfaces {R(z)} defined by the equations y2 = x(x — l)(x — z), zεC — {0,1}, we have one independent abelian differential ω = y−1dx on each R(z) and if we consider z as a parameter on C — {0,1}, the integrals are solutions of the Gauss’s differential equation