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On the self-linking of knots. (English) Zbl 0863.57004

Summary: 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 E. Guadaguini, M. Martellini and M. Mintchev [Perturbative aspects of Chern-Simons fields theory, Phys. Lett. B 227, 111 (1989)] and D. Bar-Natan [Perturbative aspects of the Chern-Simons topological quantum field theory, Ph.D. thesis, Princeton University, 1991; also On the Vassiliev knot invariants, Topology 34, No. 2, 423-472 (1995)] 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.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
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[1] DOI: 10.1016/0370-2693(89)91291-4
[2] DOI: 10.2307/2946631 · Zbl 0820.14037
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