Abstract
There is a higher dimensional analogue of the perturbative Chern–Simons theory in the sense that a similar perturbative series as in 3 dimensions, which is computed via configuration space integral, yields an invariant of higher dimensional knots (Bott–Cattaneo–Rossi invariant). This invariant was constructed by Bott for degree 2 and by Cattaneo–Rossi for higher degrees. However, its feature is yet unknown. In this paper we restrict the study to long ribbon –knots and characterize the Bott–Cattaneo–Rossi invariant as a finite type invariant of long ribbon –knots introduced by Habiro–Kanenobu–Shima. As a consequence, we obtain a nontrivial description of the Bott–Cattaneo–Rossi invariant in terms of the Alexander polynomial.
Citation
Tadayuki Watanabe. "Configuration space integral for long $n$–knots and the Alexander polynomial." Algebr. Geom. Topol. 7 (1) 47 - 92, 2007. https://doi.org/10.2140/agt.2007.7.47
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