ON THE SELF-LINKING OF KNOTS

This note describes a subcomplex F of the de Rham complex of parametrized knot space, which is combinatorial over a number of universal ''Anomaly Integrals.'' The self-linking integrals of Guadaguini, Martellini, and Mintchev [''Perturbative aspects of Chern-Simons field theory,'' Phys. Lett. B 227, 111 (1989)] and Bar-Natan [''Perturbative aspects of the Chern-Simons topological quantum field theory,'' Ph.D. thesis, Princeton University, 1991; also ''On the Vassiliev Knot Invariants'' (to appear in Topology)] are seen to represent the first nontrivial element in H-0(F)-occurring at level 4, and are anomaly free. However, already at the next level an anomalous term is possible.