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 Chem–Simons field theory,” Phys . Lett. B 227, 111 (1989)] and BarNatan [“Perturbative aspects of the Chem–Simons topological quantum field theory,” Ph.D. thesis, Princeton University, 1991; also “On the VassiUev Knot Invariants” (to appear in Topology)] are seen to represent the first nontrivial element in H0 (F)—occurring at level 4, and are anomaly free. However, already at the next level an anomalous term is possible.
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